Sorry, I assumed that you already had the mounting plate off. Btw I also assumed that you have the same chrome mirrors on your car that I do on mine. If you have the body-colored sport mirrors I'm probably not the right one to be offering advice.
Anyway, there are two holes in the door that the mounting plate attaches to and there is some sort of a threaded piece attached (glued??) to the backside of the door. (Since my experience is limited to 1 car before you go and take the bolts right out of that mounting plate you might want to back them off a bit and wiggle them to make sure that the piece that they're screwed into is securely attached to the door so you don't have to take the door apart to retrieve it.)
On my car, it's apparent that someone has moved the threaded pieces on the backside of the door as there are two holes similar in size and spacing that have been filled which are faintly visible.
When I said mine were proud of the surface of the door I just meant that they are not flush with the outer surface which means that the mounting plate doesn't sit flat on the door. Of course, the stability of the mirror is dependent upon the bottom of the mirror being tight up against the door and in order to for that to happen the mounting plate has to sit flat on the door. Since the mounting plate is sitting higher than it should be (about 1/8")there's a gap between the bottom of the mirror and the door and that's why mine wobbled.
So, I happened to have a replacement black plastic gasket that fits between the mounting plate and the door. and since they are sort-of flared on the outer edge I thought that the extra thickness may be just enough to give the mirror the support that it needed. Which it did. Oh, and the gasket is just wedged between the mounting plate and the door, nothing remotely tricky about it.
Yours may be wobbling for a different reason, but if you've checked the mounting plate and it's ok, and the mirror is ok and you're able to tighten everything as it should then this might work for you too.
I hope this helps. If you need more clarification don't hesitate to ask.