So, after extensive searching around, I can't find anybody else who has this problem. This happens in both Crysis 1 and Crysis 2, however it doesn't occur all the time. I have no idea what triggers it in Crysis 1, but in Crysis 2, it happens when there is a map change on multiplayer (I've hardly tested singleplayer). When I join a game for the first time, the maps appear to be working as they should. However, when there is a change of map, the LOD in the game completely screw up with objects only just changing to their highest detail level when I'm very near them, and the transition is very noticeable. This is greatly ruining the experience of the game for me of all things.
Here is a video demonstrating the issue on the map Lighthouse: http://www.youtube.com/watch?v=c4mn3TT8K9Y&feature=channel_video_title
Every single other game for me works just fine. Crysis 1 and 2 (and possibly other CryEngine games) are the only games giving me this issue. Interestingly enough, I only recall this occurring since I had created an autoexec.cfg on both the games. Crysis 2 I had done so with the advanced tweaking tool. However, removing the autoexec.cfg does not resolve this, the problem just sticks. I haven't tested to see if uninstalling and reinstalling works yet.
Also, this may or may not be related, but in Crysis 2 (but not in the demo or Crysis 1, where I DID NOT encounter this issue) I also get some slight flickering textures. Specifically, on the main menu, the water and some foliage. This can also be seen in the video.
I can only suspect this has something to do with way the HD6870 renders the games, although reviews of the card suggest otherwise. I have the latest drivers installed. I thought it might be the Catalyst AI (which since some driver update can not be disabled) causing this issue, but again, I can't find anywhere else where somebody is having this issue.