EDIT: Fawfulfan beat me to it. If you see SUPAA1 and such, pretend his post says SUPA instead of PLAY.
You're copying sprites out of another WAD, right? OK. When SLumpEd loaded that Super Sonic WAD, it messed up some of the sprite names, because SLumpEd is stupid like that. The falling animation sprites are SUPAA1 and so on, right? Once you paste them into your WAD, rename those sprites to SUPAa1, SUPAa2a8, and so forth. Same goes for the grabbing-on animation. SUPAb1 and so forth.
All in all, SLumpEd is a bit tricky when it deals with ANYTHING regarding Character WADs, because of its glitchiness.