Was This An Egregiously Lenient Sentence? Yes.
Did he get lighter punishment than he "should have" (in some sense)?
A six month sentence for a non-negligent homicide was virtually unprecedented then and remains extremely low.
Even a six month sentence for the rape of an adult woman (which is generally a comparable or less serious offense than manslaughter) by a privileged white offender generates immense controversy today as it did in the case of the sentencing of Brock Turner for that offense in 2016 (something that ultimately cost the judge imposing that sentence his job).
There is no way that intentionally hitting someone is negligent homicide. It is at a minimum reckless, and honestly, is hard to see as anything other than intentional conduct. While it wasn't premeditated and hence wouldn't qualify as first degree murder eligible for the death penalty, this would be a fairly straightforward case for a second degree murder charge and a sentence of a decade or more.
The intentional part apples to the act of hitting someone, not the result of causing their death. This intent was present here.
Where Did The System Fail?
in what way did the legal process fail? Or do you think that there was
any failure at all in the legal process?
Was the substantive law at fault? No.
The substantive criminal law in 1963 was very similar to what it is now and would have authorized a much more severe sentence on the crime of conviction and would have made a more serious charge of murder viable.
Arguably the substantive law should have had a mandatory minimum sentence for homicide, but since judges very rarely impose such lenient charges for homicide in cases like this one where there was no good reason for leniency, many states don't do that now and it isn't a problem that legislators would reasonably have believed that they had to worry about. Allowing leniency in some extraordinary cases that capture considerations that the law does not expressly mention is often a good thing, rather than a bad one.
Did The Appellate Process Fail? No.
The defendant's conviction was not wrongfully reversed on appeal, and it is generally not possible for a defendant's sentence to be increased on appeal in these circumstances.
Arguably, this is not an ideal rule of law (and it is not the law in most countries in these circumstances). But this was not a major problem with the legal system that was a primary reason causing the outcome in this case to be an exceptional miscarriage of justice.
The Judge's Sentence Was An Abuse Of Discretion.
The judge imposed a very light sentence within the statutorily allowed range of discretion.
While we can't literally read the mind of the judge and the judge doesn't acknowledge this as a basis for the sentence, given a larger pattern of similarly lenient sentences of similarly situated people given light sentences by judges, we can make a very reasonable guess about the most likely and plausible reason for the lenient sentence.
The most likely and plausible reason for the sentence is the one identified by Bob Dylan. A high status white man killed a low status black woman, and the judge felt that, as a result, it didn't justify as serious of a sentence.
The actual chain of reasoning in the judge's mind consciously may have involved considerations like the view that the victim was an "eggshell" victim, and the likelihood that the defendant was capable of reforming his conduct after a short sentence and thus didn't present a threat to the public.
But the courts very rarely grant leniency to someone on the grounds that the victim was "fragile" - usually this justifies a more severe sentence. And the documented fact that the perpetrator routinely assaulted others with his cane casts grave doubt on the extent to which he could be rehabilitated more easily than a typical defendant.
Also, even if the charge of conviction was manslaughter, this case would have been considered at the high end of the range in terms of the culpability of the offender who went around assaulting many people at a public gathering seriously enough to cause harm, and to in one case cause a death of a more fragile victim. The sentence should have been at least at the midpoint of what is allowed (currently about five years out of ten possible) in a case like this one.
Further, while Maryland is not in the "Deep South" it is a Southern state with a history of slavery and Jim Crow discrimination, and the judge in this case would have lived under and seen enforced to his benefit, Jim Crow laws in Maryland during his lifetime.
The Civil Rights movement had not succeeded to the point that racism was a completely disavowed and unacceptable form of motivation in 1963, particularly in even parts of the South outside of the "Deep South" at that time.
As a reference point, President Biden, in nearby Delaware, was starting to make a name for himself in politics at the time as a defender of segregation in the school system and an opponent of busing to desegregate schools. This issue got him elected and re-elected. Biden reformed his views later, but racism was alive and well in Chesapeake Bay area at the time.
Was Prosecutorial Discretion An Issue? Possibly To Some Extent.
The prosecution's decision to press charges for manslaughter rather than murder was also questionable, but less obviously so. Today, common practice would be to bring both murder and manslaughter charges in a case like this one. The facts would have supported a second degree murder charge.
The fact that the prosecution originally brought a murder charge suggests that it knew that the facts supported that charge, and was influenced by some political or tactical consideration, or by judicial pressure, to drop the more serious charge before trial. But without insight into what that reason was (which is much less obvious than the judge's motivations) it is hard to judge whether the prosecutor should have acted differently under the circumstances.
The fact that the prosecution pressed charges, took the case to trial, and got a conviction at all also suggests that the prosecutor's conduct was not at the bottom of the barrel compared to more racist prosecutor exercises of discretion in 1963 elsewhere in the U.S. The prosecutor had the full legal ability to decline to press charges at all without facing any legal consequences for failing to do so.
Further, while it is certainly plausible that prosecutor's racism figured into this decision, it is also important to note that the prosecutor has to consider the attitudes of a likely jury pool when bringing charges. Even if the prosecutor believes that the defendant is guilty of murder under the law, the prosecutor has to consider whether the odds of getting a conviction from a local jury that is likely to have considerable racial bias influences what charges are right to bring in order to get a maximum conviction, as opposed to what charges the prosecutor believes are legally justified.
Likewise, if the judge indicated the he would be likely to dismiss the murder charge before trial in a preliminary hearing, that would also make a prosecutor's decision to comply with an implicit judicial suggestion to stay in the judge's good graces for the remainder of this case, and for future cases before the same judge, understandable.
However, if electoral public pressure, or the defense counsel's pressure or influence, caused the prosecutor to give up on a murder charge that a conviction would probably have been secured upon, this is much more problematic and would suggest racial and status bias on the part of the prosecuting attorney's office.
Was Jury Conduct An Issue? No.
The conduct of the jury in this case was not an issue, even though the potential of jury nullification that didn't happen was a factor that may have influenced the charge brought by the prosecution. The jury convicted the defendant on the most serious charge presented to it.