BMW Repair: BMW 740i 2000, bmw 740i, rear suspension

Question
There is an intermittent thumping coming from the right rear of the car, I think the tire or wheel. There seems to be an abnormal amount of grease on the wheel itself.

Answer
Most likely something in the rear suspension (assuming you've ruled out your boss in the trunk).  There are a number of things in the rear suspension that could cause this, from the strut to the mounts to the control arms.

I can't provide much more assistance remotely on this.  Unless you've got a lot of experience with suspensions, I'd recommend taking it either to a dealer or a good independant mechanic who knows BMW suspensions.  Will be cheaper in the long run.