A series of recent court decisions and policy changes is starting to reshape how the U.S. justice system handles disputed or debunked forensic techniques used in thousands of criminal convictions.

The changes affect crime-show staples like identifications made using hair samples, burn patterns, bite marks, ballistics evidence and handwriting analysis, among others. Over the past two decades, many scientists have said these disciplines are unreliable and subject to bias, but courts and law-enforcement authorities had until...