Stuck in gear!

[BudMan]

Something has let go due to falling over.  I can see no way the clutch plates could have been damaged just from laying the scooter down.  The first thing I would check is to see that the clutch is releasing all the way.  I've mistreated a lot of machines over the years, but I don't think I have ever warped a multidisk clutch, and that includes a good number of tractors.
I'm betting you sucked a big bubble in the clutch fluid.

[Greg Cothern]

I would thoroughly clean and flush the master cylinder for the clutch etc and bleed it and proceed from there. 

Laying it over would only affect the clutch if it happened to pinch a hydraulic line, bend a linkage, etc that type of physical/mechanical damage.

Typically warped multi-disc setups will vibrate more than chatter.  If its chattering I would think incorrect oil (friction modifiers cause havoc on our clutches) or simply very worn friction discs...

If cleaning and bleeding didnt change things then I would pull the side cover and get to the discs to inspect..