You can't stop moving, but more importantly, when the difficulty ramps up high enough you won't be able to move fast enough anyway :D
An improvement would be to make it so the mouse pointer and the brush part of the mop are in the same place. Now you need to click on the mess with the mouse pointer, but the mop will be some pixels off to the side, causing you to miss the mess if you actually try to click when the mop is over them.
Nonetheless, I think I did quite well (but the background for the end screen... eeh.... :P):
Great job !