It is my opinion that much of modern LEO's abilities to solve crimes are based on maintaining a facade of authority built up by the common perception of their methods. Specifically I mean the methods of analysis like hand-writing analysis, polygraphs, and even more "scientific" methods like finger-prints or DNA evidence. These methods of investigation are often portrayed in popular media as 100% effective in providing proof, however their real rates of effectiveness are quite a bit lower.
Much of these techniques are not as effective as claimed or perceived, but are used as a tool to bring pressure to bear on criminals to cause them to implicate themselves indirectly or confess completely to their crimes.
Much crime is solved merely by rounding up the "likely suspects" and tricking them into thinking that the case is already solved and the criminal just has a chance to admit and gain some sort of ameliorative to their sentence.