Nikaidou's amazing baseball save does, as several people have mentioned, stretch if not actually violate the laws of physics.
Whaaat? She just caught the ball. It'd be hard to do, especially without looking at it, but it's nothing superhuman. It wasn't even a batted ball, it was just thrown by a guy.
Sure, if you assume she has eyes in the back of her head, world-class reflexes, and is impervious to pain. You’re right, the ball was “thrown by a guy”—an “ace pitcher” who throws hard enough to freak out the guy with the glove.
Catching a baseball thrown like that with your bare hand hurts—it can be done, but that non-reaction is crazy.
Like I said, it’s unlikely that there’s anything supernatural going on, and the “unreality” is done for comedic effect.