I don't know about proof, but in the Zazi case we saw that there were three people who were identified as connected to the plot early on who were quietly dropped from the story as it progressed, leading one to conclude that they were indeed false positives.

http://www.emptywheel.net/2013/06/15/the-inefficacy-of-big-b...

As for "robberies, murders, etc.," we know that Section 215 orders have been used against hackers, and the government themselves have described the purpose of the programs to be applied to "criminals" in general:

http://www.emptywheel.net/2013/06/12/is-the-section-215-drag...

Sorry for all the emptywheel, but she is a documentarian and thread-connector on these topics par excellence.