I've noticed the speedometer does not function

I own a 1995 Taurus GL Sedan (3.0) V6 engine. It has 112,000 miles on it. For the past few months I've noticed the speedometer does not funtion for the first 15 to 20 minutes of vehicle operation. In this time, other than me not knowing how fast I'm going, the car performs flawlessly. But after that time, the speedometer starts to fluctuate between 0 and whatever speed I'm going, causing the gears to slip and the RPMs to shoot up. It makes driving on highways very difficult and unsafe, not to mention hurts my gas mileage. I don't think the transmission itself is broken because it works fine when the speedometer reads constant 0, so I'm left to believe that whatever is causing the gear slippage has something to do with the speedometer. Any idea of what I can do?