First, I'm sure most of you have seen the video of the texture issues and we know Bethesda is working on the fix. I did notice the issue with my game installed and I am now running it from the disc.

To fix the problem with arrows stuck in the character, make sure the game is running as stated above, from disc. Back out to the Dashboard and reload the game by pressing "A". Continue holding "A" until the Bethesda logo shows on the screen (Yes, its the good old texture cache reset from Oblivion and it still works with Skyrim ). A friend of mine had the same issue and he'd started a new character to get rid of it, sadly. If the upcoming patch doesn't fix this also, now you at least have a workaround for the issue.

Another way to fix it is to get shot more so that it reaches the limit of on-screen arrows, the glitched ones will then disappear.

Perhaps, but the other way is faster.

Depends on the situation really, you could be in a dungeon full of archers which would make the solution I posted quicker but yours would be quicker if you were in a town or something.

Two methods for two situations.