The average viewer only knows so much about the science and methodology of solving crimes. If they're going to understand your Crime and Punishment
story at all, you're going to have to rely on a couple of standard crime-solving tricks. This is the Applied Phlebotinum
of the Mystery of the Week
Though shows have gotten better over the years (probably because the audience has gotten smarter or better informed), quite a few of these tricks don't actually work, or don't work nearly as well as they do on TV.