Purchased a 1999 Cougar V6 with 133k mi. Very clean and I am very pleased.
I did have the following issues: engine light, speedometer not functioning, transmission slippage, and a severe oil leak under pressure.
Engine light was some vacuum hoses. Speedo and transmission was a broken speed sensing gear - not the speed sensor. Oil leak was the oil pressure switch. All were fixed at a local (great) shop for @$300.
Love the car - the investment was well worth it. No leaks, no slippage...Other major items were already taken care of before I purchased - but thought I would share the news, particularly on the transmission/speedo fix.
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This seems to be a common problem with older 99 and 00 models from what I''ve been able to find online. There''s a discussion about it in this forum:

http://www.2carpros.com/forum/2000-m...garmercury-cou gar-bucking-vt121761.html

What does NOT seem to fix the problem is:

New spark plugs, fuel filter, carbon cleanout, new EGR valve

What DOES seem to fix the problem is:

New temperature sensor (you need to get this directly from Ford but the model for the Contour looks to be compatible), MLP (mass lever position) switch, and/or the Mass Air Flow sensor. The parts appear to be cheap, but the labor can add up to a decent amount. Hope this is helpful.

does it happen at 35mph? or so?

a bad torque converter also does this. get the trans fluid flushed out. drain all fluid even the converter and pan fluids. it should stop.