PS3 Bad Company 2 Freezing and Acting Odd?

Could be both. I had a similar problem with my BC2 on my 120GB PS3. Although my screen didn't go black, the sound was constantly out of sync with the gameplay and cinematics. Mine also froze up occasionally, usually the first or second time I tried the game, but most often when I attempted to enter Multiplayer. Returned the disc, had the system inspected, they didn't find anything, 80 bucks out the window. I exchanged the disc for a new one which worked fine for about a month, then started doing the same thing. I've noticed that the more often I play it, the more often it occurred. So I accused overheating being the problem, which I now assume is right. After playing the game for several hours, this would happen. When I restarted it, it would happen again, so I let it sit for a couple of hours, tried again, worked like new. I would say out of your given details this is the problem. It can't be the HDMI, because that wouldn't affect actual gameplay, just the visual and sound effects. Try a different game, if this doesn't happen then it's how your PS3 is trying to play the content on the BC2 disc. Try un-installing your most recent update of the Battlefield game, not the system's. Then run it again, ignore the prompt for the later update and try to play Story Mode. If the problem is gone, then it was most likely just a faulty update and you can re-install the update. If it's still there then I'd return the disc and try a new one. Hope this helps!