I was involved with training a chap with no legs to fly back at NZTG a few years ago ... he had a special crutch type gadget that used to clamp onto the rudder pedals and I must say he did a bloody good job, I would say right up with the top few percent of fully able-bodied pilots in terms of the raw handling skills he displayed.
There's also a kiwi guy that flies Dash 8s for BACE in the UK who's only got one arm.
I know one guy who would appear to have at least a mild mental handicap who regularly kicks everyone's ass down at the local motocross club. I can't see a problem with letting anyone short of paranoid delusionals have a crack at flight training, anyway ... so many of them will surprise you with what they can achieve. If they can't cut it then I'm sure the testing officers concerned will keep them out of the system.