Coming from a statistics background, it seems like there is an easy fix for many of these problems (trigger warning: p-values ahead).
For example, if you want to claim someone's fingerprints are a match for a given fingerprint from a crime scene, you need to show that the probability of a random person's fingerprints matching is small. One direct way to prove this is to get the prints of N random people, plus the prints of the suspect, and compare them to the print from the crime scene. If the suspect is a better match than N(1-p) of the other fingerprints, then the match has a p-value of p.
Even if matching is done by a human expert, a computer could be used to reduce the set of potential matches before a human was used to select the best match out of these candidates (of course, the expert would not know which one belonged to the suspect).
I know all of this is obvious to someone with a thorough knowledge of statistics, but I honestly think this is just lacking in the discipline.