I had similar problems (Live Tiles not working, mobile internet stopping randomly, overall weirdness) with my EE (UK) locked Lumia 920 on Virgin Mobile UK.
Then about a month ago decided to unlock it and flashed it with the CV GB ROM and it is as if I have a different phone.
Only thing it needs is a reboot every morning to calibrate the (atrocious) built-in battery meter.
Now everything works as it should be, the best ?35 I have spent frankly (to unlock it).
I think there is something seriously wrong with the carrier ROMS but then again it might just be my experience.