Warrants (and similar things, like indictments at preliminary hearings) rely on the concept of “probable cause”. The definition of probable cause varies, but in general requires for something to be more probable than not — or in terms of Bayesian probability (which applies probability to states of mind, not just to repeatable experiments), higher than 0.5 probability. Do our warrants actually obey this ruling? This is a fairly simple test — at least 50% of warrants handed should, eventually, result in evidence leading to conviction. Do they? Hell, in less than 50% of cases does it lead to an indictment!
Since warrant judges hand out a lot of warrants, we can decide to actually measure and automatically disbar judges whose warrant rates fall significantly below 50% rates (e.g., using p values of 0.005 would correspond to having a pretty high Bayesian prior that judges are “good”). The criteria could simply be — “of all warrants handed out where the case has ended, how many convictions have there been” (so any cases still in trial would be eliminated from consideration). After doing this for a while, we can update the Bayesian prior, periodically, to how many judges actually get disbarred by this.
In a perfect world, we would also apply this to convictions — however, since convictions are handled by one-offs (jurors), it is hard to place blame for overturning convictions. However, at least for warrants and non-grand-jury-indictments, this allows a process of automatic continuous improvement of our standards, avoiding the “judges and police co-operate to come up with lots of warrants” problem.
 Technically, since conviction is “beyond reasonable doubt”, this is a lighter standard than the true standard of actual guilt. However, based on the “better a hundred guilty people go free…” (Benjamin Franklin) standard, reasonable doubt being >=1% probability, the effect should be minor.