-Being able to choose your losing animation
-CPUs vs. CPUs
-Instead of pictures when you choose characters, maybe have animations or show their models (think Smash Bros. 64)
-Changing the models when you're choosing different colors rather than just that palette thing
-Boss Arena as a playable stage (including the stage hazards)
-More upbeat/flashy screens when starting a match, instead of just the pictures showing who you're facing
I think the animated model idea should also be extended to the loading screen. Instead of seeing static renders of who you're fighting before every match, it would be cool if the characters were animated like they are in the results screen, but instead with their own unique "ready to fight" poses.
Also, it would be cool if you could see which stage you're fighting in before the match starts (like in Xarf's awesome GIF).