So, I'm doing the "Missing in Action" quest from that old woman in Whiterun. I get out to that fort way in the NW of Skyrim and I see http://i1012.photobucket.com/albums/af244/judeferguson42/2012-11-09_00003.jpg. My first reaction was "well, that's odd, but whatever. i'll see if I can just do the quest anyway and go." However, whatever person is causing that glitch joined the battle as I sniped one of the guards and the game got incredibly laggy, so i exited out and decided to come here for help. What's causing this? How do I fix it?

That's...huh. Might be Slenderman. In which case you're doomed.

Ahem. Seriously though, looks kind of like an exploded mesh to me. Are you running any texture/"improved mesh" mods for armor or hair or anything like that? If so try uninstalling them temporarily; one may have a corrupted mesh that's causing your problem. You can try reinstalling later...though I would recommend trying to track down the mod that's the culprit and informing its author, assuming they haven't found and patched it already.

Alternatively, or if you're not using any mods like that: open the console (~ key) and then click on the Cthulhu-esque abomination. (It's large enough that you should be able to do this from a distance if lag is a concern.) Type "disable" into the console (without quotes), hit enter. Abomination should disappear. You can then also type "mark for delete" and hit enter again, which will tell Skyrim to mark that NPC for deletion and keep it from coming back if you were to, say, save and reload your game. Although I'm not entirely sure mark for deleting a live NPC who may have important scripts attached to them is such a hot idea.