Did you reset the odometer while moving? I've busted more than one doing this, although I think they were already going! There appears to be a problem with the gears binding while you are resetting them, and that causes the zinc drive gear to start slipping on the steel drive shaft. Probably a safty feature so you don't damage the rest of the speedo head.
The drive gear for the odometer is slipping, or the little star gear that flips the next plastic wheel is missing a tooth -- both are common failures.
VDO does repairs for about $100 -- take odometer out and send in, takes about a week.
There are also other places -- PaloAlto Speedometer advertizes in Hemmings Motor News, for instance (fun publication if you've not seen it!).
If it were a W115 or W123 I'd tell you how to fix it yourself, but I've not taken one from a W124 apart yet (the 300TE trip odo is broken, main odo works still), so I've not got any specific advice.
It's legal to drive the car with no odometer as long as you don't attempt to sell the car while stating the milage is actual -- you must sign an affidavit that the odometer reading is not accurate (this is on the title in Indiana, probably in other states as well).
Lots of these VDO odometers die around 200,000 miles.
You might try punching the reset button a couple times while the car is sitting still, too -- the trip odometer on the Volvo sticks once in a while when reset and won't register until I push the button again.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!