Axon has an app for citizens to report crime and upload evidence, that seems like it would go a really long way to get numbers that are at least correlated with publicly visible crime statistics, and I think that's the main goal. The published numbers are a function of real crimes committed plus how hard the law enforcement agencies and local government are trying to suppress those numbers. The Citizen app would give us the dot product of publicly visible crime and use of the app, but I feel like that's probably more reliable than what's currently being published.

Also, Seattle has a Find-It-Fix-It app that allows people to report various things that are broken with the city, opening up that data to the public would be great. I know it's not crime-related, but getting an overall sense of the health of the city seems correlated. This would require that the app be administered by a 3rd party though.