Have the transmission fluid flushed and have the computer updated. Have read that this has solved quite a few of the 2005-06 MCSa owner's problems. If you look at the other vehicles that this transmission is installed on (Audi TT, Toyota, Saab, BMW, Mercedes,...) they all have one thing in common and that is that they are not supercharged. The Saab's are turboed, but the turbo is far enough away from the transmission that the excess heat doesn't affect the tranny. My guess is that the extra heat that the SC puts off is destroying the fluid in the transmission and that is what causes the bad shifts. If it was a mechanical part such as a valve body, it won't work at start up and a few minutes after and then start acting up shortly after. The only thing it would be is either the fluid is bad or a computer issue and you stated that the computer had been updated. I am currently fighting my mechanic who is convinced that the whole tranny needs replaced, like I have 6G's laying around to throw at a car...

P.S. - I know that BMW claims that the fluid is lifetime, but the fluid is suppose to be clear, not brown and burnt looking. I believe BMW states that it is lifetime fluid because Aisin Warner claims it to be lifetime fluid. In the instances that Aisin tested the transmission on, which was on Toyota, naturally-aspirated engines, the fluid will last a lifetime. They would save themselves the headache of a lawsuit if they just recall everyone in and flush the fluid!

Mini shifting down hard/ not wanting to shift out of second
 

I'm currently having the same issue I drove fine all day long I started it up to get my daughter and it wants to shift down really harsh and not shift out of second gear then out of nowhere it runs and shifts fine for a bit then starts doing it again