I didn't think these pics properly conveyed the awesomeness of those clips, so I captured these other shots:
Now be nice guys; these are from fast running sequences with fast animation.
Oh, and here's another one for good measure. You can't really apply the above excuse here. :/
Lookin cool there Rouge
^ That's not really an animation flaw.
Chuck must be resting his feet on an invisible book or something.
That's all I've got to say about this pic...really, it is. Honest.
"Egads! The site of my grandfather has caused the red to go away from my nose!"
Wait, wasn't he on earth long before Eggman got there?
Amy's taking pointers from Rouge, apparently.
No...no, before you say anything, that's not the reason I'm posting this here. Look...look at Tails. Ignore that and look at Tails.
Edit: Pppth, hypocritical me. I could've just posted this one instead. :P
So what I found out is that in the Japanese version, Amy's actually expressing her concern that she's got marks on her butt left over from when they were being tossed in a net earlier, and Cream is assuring her that she's just a little bit red.
...Well I knew Cheese had to be blushing for some reason other than her legs being too skinny.