When I recently replaced my radio with an Alpine CD/MP3/XM unit I had bizarre electrical problems. Wipers wouldn't shut off, seatbelt extenders extended and wouldn't retract, etc. Additionally, the dome light would either stay on part time or flash. Lead me and the installer to believe the dome light was wired to be a warning indicator of some kind. We pulled the recently installed radio and checked all the connections, then reinstalled. The assumption was that in the cramped space behind the head unit, a wire or harness was either damaged or so cramped that a short was occuring.
The problem was resolved after reinstallation. It is reasonably easy to remove and replace the radio. You might even pull it and do a bench test. A good car stereo installation place will probably do this for you on a slow day for about $20.
Good luck. Let us know what happens.