Why it's Bullshit:
First, do you have any idea how much random DNA you are carrying on the soles of your shoes this very instant? A hair from that bank clerk across town, gum from a Pakistani cab driver and semen from an undetermined source are all probably crawling around down there, ready to be tracked through a crime scene.
Also, certain laboratory tests such as DNA samples, toxicology and blood reports can take weeks or even months to process, and when they do finally arrive, they are about as clear cut as the plot to The Phantom Menace.
"Wait, they're racing now?"
Also, while DNA criminal databases do exist, less than 1/10th of all criminals are a part of it. Having a bit of DNA doesn't mean s**t unless they have something to compare it to.
That means the CSI stuff is less about finding the killer and more about making sure they have enough evidence to convict the guy they've already pinpointed as a suspect through old-fashioned police work.