I found out that if I start off with the engine cold, I got the stumble. But when I let the car idle for at least ten minutes, no stumble. Go figure.

 

My morning routine is as follows:

Open garage (manually)
Start MINI
Back out of garage
Get out and stand in frigid garage
Smoke cigarette
Curse my filthy habit
Smile at my MINI running in the driveway
Finish cigarette
Close garage door (again, manually)
Get in MINI
Drive to work

On really cold mornings my steering column makes a slight popping noise/feel until MINI is warm. Once warm, it goes away.

 

I second the start it up and drive off and warm up. thats the best way to warm up newer cars... it warms up everything and not just the engine. Shift at lower RPMs until the engine oil is fully warmed up.

 

A few years back they used to warn against letting your car idle for very long as the catalytic converter gets so hot it could start a fire. That would only apply to parking on grass I suppose, but that may be the answer. Lubricants are much better and the engines are built to better tolerences so I think it is unnessesary to warm up car for too long.
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As for the stalling problem>I have that too. You just can't start the MINI let it warm for 30 seconds and drive. It will quit at the first stop sign. I have an '03 MC with original software.