Reminds me of a weird bug I had with a Gears of War 3 DLC with my 1st generation X360 console.
Try uninstalling the Omega DLC (by deleting it from your Xbox Storage) and then downloading it again (should be free since you've already paid for it) to see if that solves the problem.
If it does or if the XBL system tries to charge you 1,200pts again, contact Microsoft Support and ask for their assistance because they will be able to let you know if this is an Xbox conflict (if the problem reoccurs) and that you've already paid for it (from your XBL account records) to let you download it again for free.
(Edit: Clarified solution)
I've had this same issue since the DLC came out and I cannot find a solution tothe problem. I get about 10-20 minutes into it and it tells me the disc is unreadable even after reinstalling the DLC
