Voyage of the Little Mermaid does allow photography and videotaping as long as there is no flashes or camcorder lighting. Not only can it disorient the performers as was said, but by taking a picture with the flash, you may see more than you bargained for. The people wear black suits against a black background to do a lot of the puppetry. With flash photography, you would probably see this. For those of you who don't mind a little spoiled magic and want to see something funny, try taping Voyage of the Little Mermaid with a nightshot camera where you can see the guys, it's pretty funny and gives you a whole new perspective, but it is not for the people who want to preserve the magic. This is also true of Fantasmic.
Haunted Mansion can be taped fairly well with nightshot video cameras, at least to the point where you can see most of the effects, even though it is in that faint green glow. A .65 lux Sony camera, though rare to find nowadays, can do a good job in color, but not a great job.
I did break the law once in Cranium Command. I don't know if he didn't say it or I didn't hear it, but I thought it was free to tape for one of those reasons. Anyway, I started to tape and the CM just stood in back of me. For a minute I didn't realize why, but he tapped me on the shoulder and just pointed to the camera. I turned it off. I also got yelled at for having my camera light on, but I didn't and explained it to the CM after getting off the ride. It was the infra-red light that they could see (which appears very bright in infra-red monitors), but is not visible to the naked eye. Don't remember what ride it was.
In American Adventure, I think it seems to depend on the CM as some say no videotaping and I've heard others skip it. As a rule it is no videotaping last I heard.
Most places where no videotaping is concerned is due to copyright and presentation permissions. They usually include shows and tapes that have real stars or real music or imagery that was non-Disney created. American Adventure has the montage at the end, Cranium Command features many stars as does Ellen's Energy Encounter, and of course filming at the Studios backlots or soundstages where designated. I was kinda disappointed that they didnt allow photos to be taken in the Haunted Mansion presentation they had there.
As far as less flash photography then back in the old days, I was told that back before they revised the audio animatronic systems, many sets relied on light sensors to control what part they were to play. I do not know if this was actually true, but it would explain why some attractions no longer have such a restriction. Also it explains why Country Bear Jamboree and the original Tiki Birds would only let you use flash photography at the end of the show. Another hint was an owl they had in what is now Main Street Photo Exposition (that used to be their preview area after the Walt Disney Story) that talked about audio-animatronics and how he was made. Every once in awhile, he would turn his head toward the wall, which seemed unusual. I leaned over the railing a bit and it looked like there was some kind of light there when he did that, which may also have been that. As I said, I was told most of this by a CM that worked there at the time, but it may have been an urban legend. Does anyone know for sure?