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Aside from the map geometry rendering issues, the following problems are repeatable in ZDoom. So I have reported it over there:
http://forum.zdoom.org/viewtopic.php?f=2&t=45657
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Yes, I too get this with quite different specs (most critically my nvidia gtx285).
For those that don't recognise the map, its the very start of MAP01 of FreeDoom.
However, I get similar on MAP01 of Doom2.
Also, when I start a map with this build, all the enemies insta-die! (You can see the zombiemen clips on the steps in the following screenshot even though the zombiemen themselves are not visible.)
Heretic is similar.
Hexen, however, seems a little better in as much as there are no obvious missing textures (at least none are instantly obvious) and the enemies don't insta-die, but no sprites are being rendered and I do hear a destructible tree dying when the game starts.
Strife is different again. I don't see any sprites initially and I don't seem to be missing any textures. However, the enemies do insta-die and then the first acolyte appears (as a corpse).
In short, it's pretty broken.