Hi, I JUST got the game up and running! At first, I didn't see any terrain, (famous "black terrain patches" bug), but by changing the settings to Low it works! No more glitches like the one in the picture.

Sadly I can't get it to run at the moment. My install is missing a 32-bit dependency (tbb) that I had before. I'm trying to get it running without STEAM_RUNTIME and other games work (for instance Civ V), but Civ:BE isn't starting. I've filed a bug on Gentoo for the missing 32-bit build of that specific package. Until that gets fixed, I might not be able to run it at all.
Bug:
https://bugs.gentoo.org/show_bug.cgi?id=545190

Hi, AzP. Is it running ok with more up-to-date packages?

I'm now running Mesa 10.5.1, 3.19.3 kernel and LLVM 3.6, so hopefully the issue is gone! I haven't been able to start Civ:BE though, I will get back to you when I do.

Thx for the tip. I'm running Gentoo, so no PPA for me. But I can run git packages if I want to, but I'd rather wait a while for a stable release.

What Jose said. No problems with the vertices, just black spotted textures.
Try the paulo-miguel-diaz ppa. Mesa and LLVM git

Maybe you should try updating to some more mesa and LLVM versions (if on *ubuntu, look for Paulo Miguel Dias or Oibaf's ppa). I'm on mesa 10.6 and llvm 3.7 and I don't get the vertex problem. I only get the black patches than also show in your screenshot.

Still played for 3 hours though... :D