You can videotape shows, like Horror Makeup Show, Ghostbusters, Beetlejuice's Graveyard Revue, etc. They even encourage it.
Rides are a different story though. My cousin tried videotaping the Cat in the Hat ride too, and the ride completely stopped at one point. She continued videotaping not realizing WHY they stopped

but then turned it off, and it started going again. She started up videotaping again. lol.......
If you can work out the timing, maybe you can videotape when your group is on Popeyes, or Dudley Do-rights. You can capture part of the ride, depending where you stand. The coasters are the same thing.
But being on the ride, and videotaping...I don't think so
Oh yeah! Videotape any encounters with the Mystical Fountain at IOA!!! So funny!!!