To be honest, it seems to happen to me more often as Falcon than any other character, and I'm not sure why. Ness' skyscraper stage (the one with the UFO... I think it's Fourside) has those two buildings on the right side, where it seems to happen more than on any other stage - save yourself using an up+B move to get over an edgeguarder, but then you don't have enough umph to get to the ledge on the center building, so instead you take the plunge because the game won't let you grab the left edge on the right building.
Definitely doesn't happen every match, but it's certainly an annoyance I'd like to see fixed.
EDIT: In response to the whole "moving stage" thing, I completely agree. Big Blue, despite its hecticness, is one of my all-time favorites (on the other hand, Brinstar and Brinstar Depths certainly aren't. Please let Samus' stages not suck this time...). Also, bring back Hyrule Castle and Temple as past stages. Just sayin'.