Jonah, I can’t help it because of my background: this kind of stuff always reminds me of proving a case as a prosecutor. You end up putting on many tainted witnesses — people who were complicit in the crime, have criminal records, have committed other acts of dishonesty, are testifying in hopes of leniency, are testifying in exchange for money, are law-enforcement types or experts who only ever testify for the government and whose promotions/continued retention arguably depend on successful prosecutions, etc. This is reflected in the distinction in the government’s disclosure obligations: the prosecutor is required to provide the defense with both (a) exculpatory evidence, which is relevant to the question whether the defendant has committed the crime charged, and (b) impeachment evidence, which is relevant to any bias the witness may have to slant his testimony in favor of the prosecution.
What you notice after a lot of years of doing this is: no matter how unsavory the witnesses are (or seem to be), if the defense lawyer spends lots of time focusing on the impeachment evidence — beating up on the witnesses’ warts — but demonstrably less focusing on the issue the trial is actually about (viz., did the defendant do what the indictment claims he did?), the defense lawyer loses. It’s not that juries decide the witnesses don’t have some biases; it’s just that eventually, if you just dwell on their potential motivations but fail to discredit the details of their fact-testimony, then the juries draw the commonsense conclusion that it’s you who can’t defend your position.