Strangely, it has started working on startup now. Here is a new debug.err in which I started the game, went to the particle cauldron, loaded and played a few things, used alt-tab, opened it again, tried loadings stuff (didn't work this time) and then quit.
http://pastebin.ca/1926173
Here is a bug I just found recently. When I'm in game and alt-tab then maximize the game again it will crash.
http://pastebin.ca/1926178
And no, I have not tried running it on lower resolutions. I can play Starcraft 2 on maximum with no problems so it should not be an issue. Would it help in some way to do so?