If my cell phone is very close to my TX it will make my plane go crazy when it rings, and for some reason it's even worse when it gets a text message. Turn on your TX, turn on your plane, and put your phone down next to the TX. Then call your phone and see what your plane does. It's not strictly radio interference, it's the cell phone signal getting in to the whole TX and making it transmit garbage.
The local police dept's mdt's will interfere with the plane itself (not the TX). If my plane is on the ground near the back of a patrol car it will jerk and twitch with each transmission from the mdt (and they transmit more frequently that you think, not just when a message is sent but there is a "received" message it sends back for every message it receives and they also pumps gps data back to dispatch through the mdt system).
All of these interference problems drop off radically with some distance.
Steve