Having bought Fez only yesterday in the sales, I had experienced the loading crash today. Restarting the Xbox failed.
After searching the web, it turns out that the last patch introduced a new bug: "if you save in the 'Waterfall' level and exit and restart the game, it freezes."
Now, if you were unfortunate enough, like me, to exit on Waterfall and encounter this bug, fret not for there is a simple solution.
- Head on over Settings -> System - > Storage.
- Highlight and press Y on the location of you Fez data (Hard Drive)
- Press 'Clear system Cache' to wipe the patch from your data.
- Next, you are going to load up Fez again, and continue from your last save, returning you to the Waterfall level. (Or any level)
- Move Gomez to another level, through one of the doors on the levels.
- Exit Fez to the Dashboard, and re-enter Fez, downloading the patch in the process.
This will have fixed the load screen crash. And you just need to remember not to exit on the Waterfall level ever again, or you will need to repeat this process.