I am fairly certain that it was on the 1000th kill Cait Sith got his limit break here, though I can go back and check if in fact it was the 999th kill. *using Master Tonberry's Everyone's Grudge attack formula* I have old save files to check this.
Edit: Yes, it is definitely on the 1000th kill Cait Sith earns his Lv3 limit breaks. Don't know what else to say about that.
When I used Mime to mimick the failed Limit Break, due to lack of MP, what happened was that no action was performed. The game essentially freezes because it's waiting for Cait Sith to perform an animation which doesn't exist, and here the game does not resort to the "Not enough MP" message. What's interesting though is that the standard 'Limit surge' animation was not performed when I used Mime.
It is not unheard of that an attack requires more than 255 MP.
See GarlandTheGreat's video on Rare Enemy Attacks, at the beginning he makes an enemy perform an attack that requires 65535 MP.
http://www.youtube.com/watch?v=3YVU6gHtkyYBut I am honestly more interested in finding out if other Glitch Limits like these exists in the original japanese release. Since I'm not up to the task of killing thousands of monsters with every character and trying out every limit an insane amount of times, I thought there might be a way to read the game's files and figure this out the easy way.