Is There a Way to Repair/Recover Corrupt Video Files?

I'd say something's wrong with your phone for occasionally making corrupt files, and/or some connections like with external miniSD card.  I've gotten the message only once or twice, but it seemed to fix itself when I browsed later, at least I don't think I lost a video/picture yet.  And when you try to copy the file and get that message, does it still let you?  If not, try a couple ways to download it from phone to pc, and move it on the phone too.
Once you get it to your pc, you can try to run some applications on it.  I know just opening VLC on it can detect some errors and have a repair feature, but that may just be for avi's.
Sometimes the phone just needs a good restart, or a software refresh, which you may be able to ask support about.  But if it continues to happen a lot, get the phone replaced.