I had the exact same problem as you when I first put in the game. The game would randomly send me back to the main menu, and it wouldn't be able to load maps in multiplayer.
I cleared the cache, deleted all Halo 4 data from the HD, unplugged and plugged back in by HD, and started all over.
After that, it worked perfectly until yesterday (I got it at launch) when I beat level 6 on Heroic and was sent immediately back to the main menu with level 7 unlocked, but level 6 showing as unplayed. Pretty frustrating.
I'd clear the cache, delete all Halo 4 data, take out and put back the HD, and start over. That mostly did it for me. But, since the same thing happened to me, I think it might be a common issue with the game.
Have any of the staff indicated whether or not they'll be reviewing the game? I know they don't review every game, even big releases, but Ryan's seemed pretty into the series and has done stuff on the past few.
I know one can get a pretty good idea of what the game is from its overall massive coverage and Giant Bomb's quicklook, but sometimes it's just nice to have a final word from a source you can trust.