

The only form of "international law" that could apply here is the European Convention on Human Rights. However, every jurisdiction has some system of appeals, apparently even North Korea. You have to file a motion for an appeal in a timely fashion. 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. 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). It may turn out that the appeals court will find that the error was insignificant so the judgment may be upheld.

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). 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. 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. It is pretty standard that you do not have an unfettered right to appeal.
