I was just playing though "Drums of War I" mission 3 "Dropping the Sledgehammer" and a background planet had a black square around it. A moon that is also shown in the background is drawn fine though.
I also tried replaying the mission just in case, but the it looked the same as the first time.
Since I never played through Drums of War in any earlier build, I can't say wether this is due to 3.4b.
In case you need it, my graphics settings are this:
OpenGL 1280x1024, 32 bit, Trilinear filter, 4x anisotorpic Filter
-ambient_factor 65
Boxex checked in "Graphics"
Enable specular
Enable glowmaps
Enable enviroment maps
Enable jpg/tga textures
Enable mipmapping
Disable motion debris
Apply Lightning to Missiles
And I used the INF build that came with the installer (when I played through the EAW Demo I used the "normal" 3.6.9 build, but switched to the INF build since, because I read it was needed by some campaigns).
Since by browser is complaining about there not being enough free space to attach the screenshot directly to the post I uploaded it on ImageShack instead:
http://img259.imageshack.us/my.php?image=tbp34bplanetblacksquareoz0.jpg