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.
Examples: