VPI Classic

I recently purchased a VPI Classic and a Benz Micro Gullwing SLR. I am having a problem with the tonearm. When I play a record the tonearm wobbles back and forth. I had my dealer look at it, and they are not sure what is causing this problem. We looked at two other VPI's and they looked rock solid while playing compared to mine. I have tried calling VPI numerous times to see what they have to say regarding this issue, but have not been able to get through to them on the phone.

I have tried adjusting VTF from 1.9 to 2.1 with no change to the wobble. I have tried adjusting the Azimuth numerous time, and it still wobbles. Does anyone else have this issue? Is this normal? This is my first unipivot, so I am not sure if this is typical.
If you are still having issue, you can debug yourself.

Does it wobble when the platter is not spinning but music is playing (play CD for example). If yes, it could be some feedback vibration from floor.

Does it wobble when the cue is up and platter is spinning? If yes, could be from the motor of the table.

You get the idea.
Seems like there could be a few things going on with your setup, but I'm still a little unclear on the plane in which the cartridge is wobbling. You said "back and forth," but did you actually mean "side to side" as in sides of the cart moving up and down, like a row boat when you rock it? Unipivot tonearms are very susceptible to any type of vibration and are rather unstable by design; that sharp spike is the only point where the entire tonearm articulates with the base so the tonearm has nothing to provide stability to it. In ideal conditions, it is not a problem, but if your table is not isolated well, it will wobble. It's simply the nature of unipivot tonearms. I used to own a VPI Scout and now have the Classic, and the Classic, even though in a different league, is not immune to mechanical vibrations that cause the cartridge to wobble unless it's perfectly isolated. I live in an apartment building that has rather "live" floors that carry vibrations easily, and I noticed listening at night results in almost no wobbling whatsoever, but during the day the cart wobbles slightly here and there, but it does not affect the tracking ability or sound. If you don't have it already, I suggest putting the equipment rack on a slab of concrete (or 4 thick concrete tiles, about $2 each from Home Depot), then putting the Classic on a maple block and the block on 4 Isoblocks. It worked great for me.
The the rear of the tonearm was wobbling like a bell. The damping fluid seems to have help with that. It will wobble for about 10-20 seconds and then it settles down with very little movement. I am using a salamander rack at the moment, but I think I might try to squeeze my Levinson 331 amplifier on the bottom of the rack for more stability. The rack is rather tall with my table on the top which is quite heavy. Maybe that will help further stabilize my table. All of the heavy components are near the top of the rack.
It does seem rather strange and I never heard of this problem before. I'd still suggest isolating your rack by putting it on an inert, heavy and solid base, and putting the Classic on a maple block. VPI recommends a maple block under its tables and for a reason--the improvement is not subtle. At least for me it wasn't. I would also double check the tonearm for any defects and the VTF and VTA settings, as well as the azimuth. If it was my table, I'd also take the tonearm to the dealer and put it on his Classic at the store to see what happens. If it doesn't wobble, you'll at least know it's not the tonearm.
Quite simply give it back!

I use a VPI Classic with no problems. I had a similar problem though with my older Linn/ Naim ARO. I think the ARO is so lightweight that the swaying effect is going to happen. The 10.5 on the VPI is pretty 'massy' so this shouldn't happen.