After turning left and accelerating out of the turn, the right side of the car wobbles/shakes. But if I continue to accelerate it goes away. I will say though, I have been having trouble with getting my MINI properly aligned. A pain in the butt. I think it might be a bushing but I wanted to get some thoughts on it.

Also, There are no extra noises (grinds, squeaks, what not) going on and my wheel bearings are not showing signs of being bad.

It's weird.

 

Tire wall failure, control arm bushings (any bushing in the strut area really), warped control arm/upper strut mount, warped axle ... I'd venture for the bushing or a tire wall especially since it goes away. Did you run up anything -- hard curb hit or run up any embankments on one side?

 

I had a similar issue with my old tires... changed them and it went away.
I'd have the bushings / suspension components checked out first though.

 

I am also leaning toward a bad bushing. Had my tire looked at and there is no indication of tire wall failure or bulging and there still is good tread left on it. I am taking it up to the mechanic soon to be inspected and driven so I can pin point the problem. If it is a control arm bushing, I'll probably get them from MINIMania.com with them already installed in the brackets. Should save time and money on that I hope that would fix my alignment issue.

http://new.minimania.com/web/Item/NM.../InvDetail.cfm

 

So. I went to the mechanic and had him inspect it. Looks like I have a bad tie rod end. Explains my alignment issues and wobbling. I was quoted a total of 401 dollars for all the work. NO WAY. I can purchase a Beck Arnley tie rod assembly with discount for 83 dollars, install myself and take it to the shop for an alignment for 45 dollars for a total of 128 dollars!

 

Tie rod? Learned something today. What was bad about it?

 

The ball joint is really bad. Told me I shouldn't drive my MINI until its fixed or I could get into a terrible accident. He said that the MINI tie rod assembly isn't made to come apart so I should just replace the whole thing. Which I plan on doing.

 

That makes sense. Glad you found the problem!