So, there's a very private Halo 4 beta going on right now. Some terrible footage leaked out a few days ago, and today, there's some more for you to take a look at. On the plus side, this clip is almost watchable!
In the first video, the users were so paranoid of Microsoft spotting their usernames on the screen that they went back in time to 1986, shot it on VHS from half a room away, then doused the whole thing in a woeful soundtrack. It worked, I guess, but it wasn't pleasant for the rest of us.
This second one is relatively better. It's still crummy footage, but you can at least see what's going on, and even see some new stuff towards the end (the grenade pistol thingy).
While it's been confirmed that a beta is ongoing, given the quality of this clip we can't be certain it's legit, so take it with a small, blurry grain of salt.
UPDATE - The original video was taken down from YouTube, but here's a second copy for posterity's sake.
Halo 4 Gameplay Preview [HaloLessons.it, thanks Harry!]