Bethesda has said to hold off on installing Skyrim on Xbox 360 due to the way dynamic streaming of the game’s textures is handled by the console.
According to the developer:
“We’ve seen a few reports of certain textures temporarily scaling down on the Xbox 360, and not scaling back up. We have verified that this issue does not occur when playing off the disc and when the game is fully cached (not installed).
“Skyrim makes heavy use of the Xbox 360 caching system, and caches over the normal course of play while in menus or interiors. This cache can be wiped when other games are played or when the user manually removes it. We’re working on a solution in the next title update for those who have installed the game.”
So, to recap: play it from the disc until the patch is issued. It will make your game run and look better.