I am asking from the standpoint of international law, has the right of appealing against a judgement become a part of customary international law? What if one is wrongfully held liable in a civil case, after a trial ridden with errors; would it be a human rights violation not to have the ability to appeal against the judgement?
Article 14, Section 5 of the United Nations International Covenant on Civil and Political Rights provides:
Everyone convicted of a crime shall have the right to his conviction and sentence being reviewed by a higher tribunal according to law.
Your question, though, asks specifically about appealing the decision in a civil trial. I don't know of any treaties or principles of international law that require an appeal in civil cases.
It is pretty standard that you do not have an unfettered right to appeal. An appeal requires that the judge committed a legal error, so if you came up with a better argument for your side, or think you have better evidence, or just don't like the outcome, you don't have a right to an appeal. If the judge improperly barred evidence, or gave incorrect jury instructions, or in a bench trial misinterpreted the law, you have grounds for an appeal. The trial doesn't need to be riddled with error; what's required is that there be an error, and that you or your attorney objected (including saying what the legal error is). It may turn out that the appeals court will find that the error was insignificant so the judgment may be upheld. Also, prosecutorial misconduct need not be (and often cannot be) objected to at the trial (especially when it involves withholding evidence, a fact that may not be learned until much later). You can file an appeal no matter what, but if there was no objection at trial or if the objection is frivolous ("Objection your honor, it's too hot!") you won't actually get a hearing. You have to file a motion for an appeal in a timely fashion.
However, every jurisdiction has some system of appeals, apparently even North Korea.
The only form of "international law" that could apply here is the European Convention on Human Rights. Though this is binding only on the 47 members of the Council of Europe, other jurisdictions do in practice take notice of its provisions, if only because Council members are not permitted to extradite suspects to countries where their human rights are not guaranteed.
Article 6 of the Convention guarantees the right to a fair trial, with certain minimum rights. This applies only in criminal trials, and the right to appeal is not included (though obviously a system that cannot correct errors would be unlikely to be deemed fair). So no, there is no universal right to appeal.
Another point that may be relevant is the difference between 'right to appeal' and 'grounds for appeal'. As user2726 says, every jurisdiction nowadays recognises the right to appeal in some circumstances, but that does not mean that any dissatisfied litigant anywhere can go to a higher court; otherwise many (most?) cases would ping-pong their way to the highest court available, enriching lawyers but ruining both citizens and the court system. So there are rules about what qualifies as a permissible appeal, independent of the facts. If the judge told the jury you are a liar that is grounds for an appeal, at which you may or may not succeed. But if the jury's verdict included a statement that you are a liar then that, however regrettable, is not grounds for appeal: it is the jury's function to determine the facts, and no appeal court has power to decide that you are not in fact a liar.
Appeals Of Civil Judgments Under International Law
[F]rom the standpoint of international law, has the right of appealing against a judgement become a part of customary international law?
No. Rights to appeals of court judgments are strictly a matter of domestic law and binding treaties.
What if one is wrongfully held liable in a civil case, after a trial ridden with errors; would it be a human rights violation not to have the ability to appeal against the judgement?
In U.S. jurisprudence, constitutional rights are almost entirely negative rights to have the government refrain from taking some sort of "state action" against private individuals or another governmental body. And, arbitration agreements are deemed to be voluntary arrangements between private individuals, which don't involve "state action" and hence don't implicate constitutional rights.
Thus, civil lawsuits are largely not subject to scrutiny for violations of constitutional rights, which are the main way that human rights concepts are given effect in U.S. law, so the notion of rights in connection with a civil lawsuit as human rights is a foreign one in U.S. jurisprudence.
This flows from the underlying political theory that governmental bodies can't be trusted to be fair towards their subjects without legal limitations on their powers, but can be trusted to enact laws through the legislative process that adequately protect non-governmental persons from each other.
This is in contrast to the larger global human rights concept that the government (and arguably anyone else who can exercise power comparable to a government) has an affirmative duty to prevent the violations of an individual's human rights by another private party, and that some human rights are positive rights that are economic in nature (e.g. a right to sufficient health care and education).
For example, in most of Latin America there is an individual right to have the government utilize law enforcement and the criminal justice system to take reasonable measures to protect private individuals from known threats to commit crimes against them and to use law enforcement and the criminal justice system to punish people who harm that private individual. In contrast, under Castle Rock v. Gonzales, it is well established that under U.S. law, law enforcement has not affirmative duty to take any action to prevent crimes or to punish people for crimes that they have committed, even when they have clear notice of the threat or clear evidence of guilt.
Most of the obligatory constitutional rights that are also human rights in civil lawsuits in the U.S. involve the constitutional rights under the 5th and 14th Amendments to "due process of law."
This said, one can imagine a situation in which involuntary arbitration or civil rules are made in a legal process so arbitrary and capricious that it would amount to a violation of any meaningful right to due process under the law, or to an arbitrary deprivation of property, which could be a violation of the U.S. Constitution or of one's international human rights to own property (since the primary effect of a civil judgment is usually to take away one's property).
For example, if the legal system routinely used involuntary arbitration process for civil legal disputes that decided legal disputes where there was an attempt to collect debts based upon drawing lots, rather than with a good faith effort to resolve the disputes on the merits, this would probably constitute a violation of both the U.S. constitution and of international human rights laws (although almost no international human rights laws are "self-executing" in the U.S. Court system and hence have no direct binding effect).
With very limited exceptions, largely limited to constitutional limitations on "body execution" for non-payment of debts, personal jurisdiction rules, and notice requirements in civil lawsuits between non-governmental parties, the invocation of the power of the courts to enforce the rights of private parties in civil lawsuits is not considered "state action". Also, constitutional protections generally do not apply in U.S. law to self-help remedies authorized by law like possessory liens and the right to repossess property subject to a mortgage or an equivalent security interest in personal property.
There is also arguably an emerging human rights principle that imprisoning someone for inability to pay a debt or amount of money (but not willfully refusing to pay a debt or amount of money that someone is lawfully required to pay when that person is able to do so), is a human rights violation, in part, because, once someone is incarcerated, concepts governing criminal justice as opposed to those governing civil disputes start to come to the fore and the state involvement in maintaining de facto or de jure debtor's prisons looms much larger than state involvement in other means of enforcement civil judgments.
Another quasi-criminal context in which there is an emerging sense that there is or ought to be human rights protections or constitutional law protections for individuals in civil cases involves "civil forfeiture" in which property suspected to be connected to criminal activity is seized in circumstances with very limited due process.
Thus, in civil cases in the U.S., arbitration awards generally cannot be invalidated merely because there were myriad mistakes of law and fact in the decision. There would have to be something more, such as bribery of the arbitrator the fundamentally undermines the heart of the private arbitration process.
Also, historically, many U.S. jurisdictions have from time to time, greatly limited the ability of litigants to appeal civil judgments entered by limited jurisdiction courts where the amount in controversy is small.
This isn't to say that people have no appeal rights or other due process protections in civil lawsuits in the United States or elsewhere. It is simply the case that these rights arise by statute and court rule, rather than being framed as "constitutional rights" for the most part. Despite the lack of a right to a direct appeal of right of civil matters under U.S. Constitutional law, there is, in fact, a right to a direct appeal of the final judgments of almost every civil judgment entered by any state or federal court in the United States under statute or court rule, even though it isn't considered to be a human rights matter in U.S. jurisprudence.
Likewise, despite the fact that all but a handful of these forums eliminate the right to a meaningful appeal of the merits of the dispute between the parties, there are certainly many contexts where arbitration of civil disputes is knowingly and willingly agreed to by private parties who establish contractual and institutional protections sufficient to provide some kind of due process, through contractual limitations, private arbitration rules, and institutional arbitration bodies. These include the American Arbitrator's Association, the Judicial Arbiter's Group (that mostly uses state court civil procedure rules), the Roman Catholic Canon Law courts, Labor-Management arbitration arrangements in union shops, international commercial arbitration forums, and rabbinical courts like the Beth Din of America (BDA), and the FINRA arbitration system. Private binding dispute resolution that is free of tight contractual or institutional constraints is the exception rather than the rule. Many countries (although not the United States) also materially limit when binding arbitration agreed to prior to a dispute in which there is no meaningful opportunity for an appeal is permitted.
U.S. Constitutional Law And History Regarding The Right To An Appeal
While not precisely on point, in U.S. Constitutional law (as opposed to international law) there is no constitutional right to a direct appeal of right in any case, although there is a right to bring a federal court petition for habeas corpus to collaterally attack a conviction of a crime (on much narrower grounds than would be allowed in a direct appeal) once all state law remedies have been exhausted to challenge a state law conviction, in the absence of a Congressional suspension of this right in a specific geographic area for a specific time frame, which it only has the authority to do where the courts are not open and operating, for example, because they are in a war zone during a civil war.
However, if a direct appeal is made available, U.S. Constitutional law imposes various legal requirements related to it.
Historically, proof of conviction of a crime by a court with jurisdiction over the case in which even remotely regular proceedings were conducted was sufficient to defeat a habeas corpus petition in the vast majority of cases (a standard of review similar to the review given by courts of arbitration awards today).
Direct appeals of convictions of federal crimes were not permitted as a matter of right until the 1890s in the U.S.
Acquittals continue to be immune from appellate review in the U.S. criminal justice system, unlike the criminal justice systems of most other countries (although the U.S. employs the ability to bring civil lawsuits and the ability of the state and federal governments to prosecute the same conduct as separate sovereigns as a safety valve in egregious cases of wrongful acquittals).
Many smaller U.S. states which lack intermediate courts of appeal still do not have a right to a direct appeal of right in criminal cases that do not impose the death penalty. Instead, in these states, there is a state supreme court with a right to consider appeals of trial court convictions on the merits on a discretionary basis similar to that of the U.S. Supreme Court.
This is one reason that in days before the right to a direct appeal of right from criminal convictions was well established in most jurisdictions, that Governors and Presidents and Boards granted the pardon power, exercised that right much more liberally than they do today, albeit, in a much more political and ad hoc manner.