I was fooling around with Pokemon Trainer and I found 3 glitches
"Eyelessaur" If Ivysaur stands on the right edge and does his near edge animation, his eyes will be missing.
"Groundizard" The dessert Mario stage has this one stair (forgot which one, but it is a bottom step) that if Charizard lands on it, he can't jump.
This last one made me go WTF. On Delphino Plaza, if you use Triple Finish when the platform is about to land, the Pokemon will fall below the stage. I was Squirtle when this happened.