My 02 S occasionally will not drop the window slightly when I open the drivers door. Of course that makes it impossible to close the door without turning on the key and lowering the window manually.
I know she's getting old (174K) but I don't want to send her to the crusher yet.
Any ideas on what part or parts may be wearing out?

 

Early MINI's are well known for having problems with the window motor. I have had both of mine replaced.
You can use the hit the door panel method or simple have them replaced (or live with it until it fails).
With 174k you have been lucky to go this long without a prior problem with the motors.