I had a Soarer some years ago. It was the 4.0 but appart from the engine I think most of the rest of the car is similar.
Problems I had were new fuel pump. Leaky power steering pump (which leaked into the alternator). Broken window regulator. I had the air suspension which needed some work on it too towards the end, problem with one of the sensors. Other than that it was pretty fast, superbly comfortable and great to drive.
I have a Supra TT which has a similar engien to the Soarer TT, just a little bigger. I've had this car for 5 years and not had one single problem with it.
Toyota make great cars and I include my LS400 in that.
Go ahead, I don't think you'll regret it.
If you don't buy it then maybe I will :D