Speedometer Issue - 1995 Police Interceptor

4.6 V-8 88000 miles. Just got the car at police auction for $1100. What a bargain. It was a sergeants car in a tiny local village. Runs great with all new tires, rebuilt front end last year and rides like a limo. Except for the spotlight you would swear its a luxury ride.

Anyway we bought it as is so we expected some possible problems. One thing we did notice when we drove it home was the speedometer suddenly pegged and stuck at 50 mph even though we were driving it slow (maybe 25-30) on a local street. I watched the odometer and trip odometer and they seemed to tick off the miles correctly. Just to make sure we got a tank of gas and checked the mpg and we got avg around 16 which seemed normal.

Some mornings especially when its cool, we can start it up and the speedometer works fine for a few miles then repeats the same as described above. Then when we let it sit all day and get in to start it up the speedometer will be stuck at around 10-20 mph. As soon as I turn the key the needle jumps to 50 again.

Any ideas as to the cause of this mysterious activiity? If it was the speed sensor wouldn't the odometer malfunction also?
HELP!