Drive Train Slight Jerk When Accelerating
 

Model: 2003 ML 320 with 100,000 miles. A transmission place check my car and said it's not the transmission and muttered something about all-wheel drive issues. When accelerating normally or quickly, there's a jerk that results about 1/2 to 1 second after accelerating. No sound, just a smooth-feeling slight thud, like something is catching up with other parts of the drivetrain. I'm also noticing a gentle motion in shifter handle, it moves slightly forward and back maybe 1/8" and I think left/right a bit at the same time as the above is going on and I think a bit after. Accelerating slowly eliminates any feeling of the jerk in the drivetrain. I think accelerating with wheels turned sharply prevents the jerk, too. There is a loud click coming from underneath that is not timed with the above, except during acceleration. I can't say it's directly connected to an exact connection of the drivetrain by is about the same time. The same click happens when braking, right about when coming to a stop. These click are only when cold and seem to be less noticeable when warmed up.

Any ideas?

I would first suspect your motor mounts. This could cause your shifter to move. Also if the mounts are bad enough, your engine could be moving up and down under acceleration and deceleration.
Also your driveshaft center support bearing could be worn out.

The transmission specialist check the motor mounts and never said anything, so I figured they were okay. I'll have them checked again along with the center support. Thanks