During acceleration the car shakes as though a tire was falling off. Bad if done under 50mph, downright scary above 50mph. Lug nuts are tight, no obvious rim or tire damage, no leaks noticed.
I would like to arrive at the dealer with some thoughts - kept to myself of course; not impressed with the local dealer and cannot drive ot 50 miles to another dealer.
I would appreciate some "possible" causes. Oh yes, when the violent shaking starts all I do is let off the gas and the shaking totally stops!!!

 

You might as well check your engine mounts.
Even slightly loose or with a worn silent block, these things can give rather impressive symptoms.
I also have a LR Freelander which was clunking and shaking hard due to an engine mount gone bad. Stealer couldn't figure it out.
I did ... but after 6 months
If, however, the vibration travels through the steering, double check the wheels balancing also.
Good luck.

 

I also have similiar symptoms on my 04 60R. The difference is that even when I let off the gas the vibration will still be there, though it it worse when under load.

I have replaced both front wheel bearings and front drivseshafts, as well as motor mounts. Many of the annoying noises have disappeared, but this one remains.

0-40 I only feel a vibration under heavy acceleration
40-50 it picks up
60-75 gets really bad
over 80 - still there but not as noticeable.

It seem as if the problem is coming from somewhere in the rear, but I can't be sure. Engine seems to strain more than necessary under acceleration (sounds labored more than it used to)

Also have put new tires on and had balancing verified multiple times.

Getting frustrated.