I too am having this issue. I had about 10hours in game before it happened for the first time (this morning). The EA support troubleshooting advice didn't solve the crazy texturing glitches, but did help with the audio fragmentation. Just like tracsys and johnnylung, I'm running a 1st gen xbox360 that was sent to me by Microsoft after my original died from Red Ring back in 2008.
I checked the unit for excess heat right as i was able to replicate the problem in-game, and it was definitely not "overheated" by xbox360 standards (believe it or not, it may even have been cooler than usual. go figure!). when I load the game after I restart the console it "Optimizes HD Content", every time. Perhaps there is something corrupted in my "HD content" file that a rewrite isn't fixing.
I'm able to dashboard once the in-game texture goes to hell and the 360 homescreen looks completely fine. Why would this be the case if the GPU was the problem? wouldn't I need to hard restart the console in order to reset the GPU as well?
Hopefully this is just a software glitch that can be patched and not a hardware failure. Any and all help is much appreciated. I just want to play Titanfall! it kicks so much ass.
Cheers,
Brian