I've got a 2007 Cooper S Turbo Automatic that isn't performing as I'd expect.

1) The gas pedal doesn't seem to give anything to the engine for a second or two when I gun it from a dead stop.
2) I've noticed that it is shifting too soon into a higher gear resulting in a pretty bad shacking. (If I use the paddle shifters and listening with my eyes there is no problem)

I'm wondering if these two problems could be related and whether they might be sensors or something indicative of worse issues.

Any ideas?