Originally Posted by petrock
With the car running, open the hood and have a look inside. Try revving the engine a few times as you watch the motor. If the motor is abnormally shaking it could be a bad motor or transmission mount.
Another method that may reveal more than just reaving is to put it gear(easier with an automatic) hold the brakes then goose it a little. If the engine moves more than just a touch, you have a bad mount... Do the same in reverse to check the other mount. Side it tips too is the bad one.
Though in your case I doubt that is the problem. I would suspect something more to the effect of the clutch just needing to be replaced. Possibly U-joints, but I doubt it, though they are easy enough to check and probably should be checked before you take the transmission out.