Television time is expensive, and television series writers want to get as much thrilling material into one show as possible. Time is scarce, and thus, they do not want to waste time introducing a new character to the view unless that character is important. Moreover, a new character is unlikely to receive lots of airtime unless they are the person who "did it." It is important that the person "who did it" is someone the viewer knows. This leads to an important rule that often works perfectly: any new character receiving seemingly unwarranted air time is the criminal.
Consider the Law and Order episode Lunacy, which aired October 21, 2008. The writers bring into the episde an old mentor of Elliot Stabler (one of the lead detectives). This mentor began as just a helpful witness, but quickly the writers had the mentor hanging around and allowing the audience to get to know the person more than was necessary. Ten minutes into the show I announced he was the murderer, and I was right. I made this prediction simply because I thought the writers would not waste scarce time with a new character who would ultimately be irrelevant to the plot.