It may be illegal for you to record a phone conversation or Skype-like session (i.e. voice recording), unless you get permission of all parties (that depends on where you and they are located). There are "reasonable expectation of privacy" considerations that are very unlikely to apply to a phone call, but could apply to a Skype session (owing to quirks in the law). That does not seem to be a concern here.
If you publicly and falsely claim that a person did something bad (e.g. the service person), then that could be defamation and you could be sued. If the person did do a bad thing, that is a defense against defamation (accurately quoting a person is not defamatory).
There is a murky area involving anti-disparagement clauses, which are or have been found in software licenses, basically requiring you to not publicly criticize the company, as a condition for using their software. If there is no such clause, there is no first step for them suing you (for breach of contract). If you are in California, there can't be such a clause. Such clauses have been upheld at least once (Freelife International v. American Educational Music).
There cannot be laws in the US that prohibit criticism, because of the First Amendment. A corollary of this is that (in the absence of an anti-disparagement clause), criticism cannot be a tort.
Therefore, there seems to be no risk, other than annoying the company. If the company withholds service, they are in breach of contract. They could, however, be less than cooperative in future customer service incidents (customer service sometimes goes above and beyond the lowest bar of service demanded by law). There is probably a clause that allows them to terminate the agreement under certain circumstances, including "harassing" personnel. Posting a factual criticism doesn't objectively constitute harassing personnel, but you almost certainly also have an arbitration clause whereby you have to resolve disputes out of court. If they terminate your agreement for harassment, the question of whether they breached the agreement is determined by, well, you'd have to read what the arbitration agreement says.