What would cause the speedometer to start bouceing around when driving?

I think you should treat yourself to a new vehicle Joe. You are just chasing faults on this one! It is well past its sell by date.

The most common reasons a Ford Contour speedometer isn't working are the vehicle speed sensor (VSS), a faulty speedometer, or an electrical issue.

Reasons a Ford Contour Speedometer Isn't Working - RepairPal

Videos and other articles. It seems a popular fault.

https://www.google.com/search?q=speedometer+to+stop+working+on+a+1998+ford+contour

..

Right off the bat it sounds like a broken speedometer cable. As the cable spins from the gearing of the transmission it is clicking against the broken part of the cable running to the speedometer gauge. The frictional clicking is what's causing your needle to bounce around. Since the cable is probably broken and cannot spin long enough to move the odometer numbers. Raise your vehicle safely and disconnect the speedometer from the transmission. then see if you can pull the cable out of the housing. If only a portion of the cable comes out, then that should answer your question. Be careful when you disconnect the speedometer cable from the transmission as not to lose any small pieces that cause the drive mechanism to work.

instrument cluster

It could be the speedometer cable has come loose from the back of the gauge.

Check distributor connections and the coil connections as well as the coil wire .

The speedometer can fluctuate rapidly under normal driving conditions when the car's speed changes abruptly, but sometimes the needle can start swinging around the dial without any fluctuation in speed. If the hairspring comes loose or breaks, it can't hold the speed cup in place, and the result is a fluctuation in the dial. In electrical speedometers, if the circuit that counts the magnetic pulses fails, it can cause the speedometer read-out to vary from the actual speed and to shoot upward or downward without notice. If a speed sensor in the automatic transmission starts to malfunction, it can affect the speedometer and cause fluctuations. In these instances, either the speedometer or the sensor needs replacement.

Sounds like the sending unit to the speedometer is failing. This causes the speedometer to jump around and confuses the heck out of the electronics that controls your automatic transmission.

If the computer is giving you a trouble code for the speed sensor, I would check that first.
The sensor is mounted on the side of the transaxle.

most common on these were the OSS/VSS

Does your D4 blink and is your cruise control operating. When you start it does it sometimes start real rough and shake a lot? If so it's probably your ICM.