When I was directing a short supernatural thriller "Momentum," we needed to leave a camera locked off in the same position for about different twenty takes. The only problem, the camera was right in the middle of the main footbridge in the city.
it was a night shoot anyway and about 2am when we started setting up. Just as we did this a Police car turned up wanting to drive over the footbridge. My producer went up to them told them we were shooting and that they could drive over the bridge for the next two hours, could they pass it on to the other patrol cars.
Even though we didn't have either permits or permission, they apologised and turned round.
The only other run in I had was on the last shoot of the feature "No Place," when we were recreating a Bosnian War. We left word with the Police that we were shooting, we had a licensed armourer on location, but the Armed Response Team turned out on the first day, scaring the hell out of our 3rd AD.