Article 12 - Judges are elected for relatively short terms, and re-election is possible. This has the potential to bind them to politics. Judges are not supposed to be politicians; they enforce and uphold the law. That is all. Politics should not play a factor.
Potential fixes: Extend the terms to fifteen years, and/or bar re-election.
Article 42 - While counsel is allowed, it is not considered a basic right.
Potential fixes: Provide for legal counsel, perhaps by requiring the nation from whence a given party comes to provide such or, if that is not possible, appointing one.
Article 59 - Judgements still have no binding. Of course, if they were binding, that would be a severe breach of sovereignty. But given this, what's the point?
Potential fixes: Unknown.
Article 60 and Article 61 - Inadequate provisions for appeal, also inadequate protection from double jeopardy.
Potential fixes: Protection from double jeopardy is fairly easy, however providing for appeals would likely require a set of appellate judges. That would in and of itself require some structural changes.
Other - The Court appears to govern itself, for the most part. In particular, it makes its own decisions on when to dismiss judges, rather than an independent body. This makes for inadequate checks and balances on its power.
Potential fixes: Unknown; perhaps an elected panel to oversee the Court, which is itself overseen by the Court, such that the two check each other's power. Perhaps this could take the form of a second Court, such that the parties in a case may select which Court to originally try the case in, and then the other can be used as a court of appeals (this could also help solve the problems with Articles 60 and 61 above).
Other - No jury trials. This is an important feature of legal systems, as the people's check on an unfair law. A jury can refuse to convict even when a law has been proken; judges cannot.
Potential fixes: Logistics may make this one unfixable. At the absolute least you'd need a really big jury, comprised of people from all nations involved and some from nations not involved. Then there's the matter of how a jury arrives at a decision: do you use unanimity or majority, and if you use majority, should it be simple, two-thirds, three-fourths, or something else?
Other - No provision for presumption of innocence. It is unclear who has the burden of proof.
Potential fixes: Include a presumption-of-innocense clause.
Other - No provision for determing what evidence is admissible or not (a la the Fourth Amendment to tne U.S. Constitution, or similar laws in other nations).
Potential Fixes: State clearly how evidence may be gathered. As a start, perhaps the Universal Declaration of Human Rights should be brought into play here; any evidence gathered in a manner which violates this should be considered inadmissible.