Watch The Wire. Most realistic portrayal of police work I've ever seen. Lots of watching suspects and gathering string, putting the pieces of the puzzle together slowly over a season of television, dealing with disfunctional organizations and a realistically low number of gunfights.
I love The Wire. I like how it shows the boring parts in addition to the exciting parts, but let's be honest, there is a lot more field work than desk work. The Wire does not convince me that being a detective would be mostly boring.
Is it really realistic though? The Wire seems to portray only cases that are relevant to the big picture plot, and they always seem to solve them in the end.
The guy was embedded with the real baltimore homicide squad for two years or something in the 80s. Read his book, Homicide, for a more realistic depiction of the monotonous life of a police department.
The wire is still realistic, because it specifically follows a team doing a large drug investigation, rather than the general work of the dept. In the book, there are a lot more misc. trails that go cold, like you describe.
One of the best TV shows ever made IMO.