Eonik

As mentioned before in this post, and as I've mentioned earlier, more "boring" and peaceful police tasks, for instance:

Domestic disputes
Traffic accidents
Shoplifters (clothing shops have alarms, which could make a cool effect!)
Street disorders (drunk people, preachers etc.)
Issuing parking tickets
Reports on vandalism

And joining colleagues in their pursuits could also be a very cool feature.

Generally more realistic and bigger variation in calls, so it won't just be car chases with bullets flying all around, like an action movie. I think an average police officer will experience this one or two times in his entire career, and in LCPD-FR it happens every day, you get my point ?

And as another guy mentioned, the ability to call EMS for burning cars, injured persons etc. and that they will actually arrive at the scene (with a realistic delay on a couple of minutes) and extinguish the fire or start treating the injured persons.

REALISM is the keyword!