I was forced to play the game on the older white Xbox 360 model for the first few days of buying the game. There was a huge amount of issues that kept cropping up whilst I was playing on this model. One of the main issues was that while I was carrying a spell in my hand, the little graphic that represents the spell (fire animation for flames spells ect..) did not appear. I would walk around with invisible spells in my hands! I had to re-equip the spell for the animation to return.
Another problem that kept cropping up was the game not fully loading the textures right away.

However, I now play the game on a new Xbox 360 slim and the game runs perfectly with hardly any issues (Apart from the odd bug here or there)

I don't know if that information was useful to anyone but I thought I'd share. I am just glad I don't have to use the older machine anymore.

1. This hasn't happened for me or any of my friends, all using the Old Elite
2. Did you install the game onto the HDD? If so, there's your problem, there's an installation bug.

1. It was the base white model, not an Elite.
2. I did not install the game on either consoles.

It's not the model you are using that matters, there are several posts on this topic its either old is better or newer models are better, some have severe texture issues others have minor issues.

The sticky at the top says the problem is the game is not caching properly, i really dont think model actually matters.

- Edit: it happens while playing off disc too although not as severe as installed.

I have the older white model and the game runs fine.