Shaking on rapid acceleration

I recently bought a '99 Saturn SL2 with 66.8k miles and automatic trans. When I was test driving it when accelerating rapidly the front end would vibrate. The guy selling it ensured us that it was the front wheels slipping, they were bald and needed to be replaced. This sounded reasonable, but we had him rotate the almost brand new back tires to the front just to be sure then we took it back out. It seemed to have eliminated the problem...or so I though. On the way home I noticed that sometimes while accelerating through a turn and also if I accelerate slowly from stop and then rapidly it does the same thing. The front end vibrates for a second and then stops. For all my knowledge it does feel like the tires are slipping, though the tires that are now on the front are in fine condition. Someone suggested to me that it could be the transmission going bad, though there is no problem when I accelerate at a decently normal rate. Any idea what the cause could be?

it COULD be the trans. goin bad, bcuz where i work i had to drive a neon and it did the same thing...sparratically when you would accelerate, softly or not, the front end would vibrate--hard...it did turn out to be something in the transmission...i forget exactly what, but good luck...

o and you could tell when the wheels are spinning...or losing grip, because the rpms are goin up but it seems as if the car isn't accleerating as fast as it should, you would also hear at least some slippage...

most likey the tires are bald, but double check the motor mounts

Only the tires in the back are bald, the tires that are now on the front aren't bald and are almost brand new. I'm replacing the back tires tomorrow.

I know the top mount is fine but i'm not too sure about the bottom mount. I havent really noticed at what rpm it does it (if there is a specific at all) but I'll have to keep an eye out from now on.

see if it happens in reverse

I haven't had it happen in reverse yet.

Also over the last few days it's become evident that it ONLY happens when accelerating from a complete stop. If I slow down to 5mph even and accelerate it wont happen.