I hate those things as well. it happened to my VERY expensive Pinky and the Brain set, and now one of the disks keeps coming loose. I really wish they used the slim pack, individual disk holders instead of the fancy fan out box..... you can't go wrong with slim packs.
Yeah I like the slim packs way better as well, as seen with Darkwing Duck, Futurama, and Family Guy DVDs for example.
Another problem with this type of package (in some cases such as Muppet show and Dinosaurs for example) is that you have to go though one DVD to get to some others, that annoys the crap out of me so much,
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I thankfully haven't had a problem when it comes to the Muppet show dvds with those teeth packages (as Zeppo called it), but I know the feeling of these packages going wrong on you. I have all seasons released so far on South Park as I'm a huge fan of that show as well. On my season ten set, the the teeth thing is totally broken as I think only maybe two or so remain, not at all enough to hold it for disc one. Everytime I open it that disc comes right out, than I check the dvd to make sure it's ok.
That tape idea isn't too bad though, didn't think of that, I'll have to do it. But still for the money we all pay for our favorite DVDs, we shouldn't have to put that much more effort into making sure their still playable.