Ensure that you are using WAD files optimized with glBSP Utility.
Unpack port files archive to the game's directory (this was 'e:\games\doom\' in my case) and start 'Doom3DSetup.exe'
Set up 'Screen Resolution' to the best one supported by your hardware, turn on '16-bit Sound' and ensure that 'c_d3d' is selected in 'DLL' field.
Click 'Advanced' to open advanced settings. Set 'TextureMip' to '1' and 'SpriteMip' to '1'. Ensure that 'BilinearFiltering' is also set to '1'.
Click 'OK' to return to main configuration window.
Click 'Save+Run' to run the game.
I've not been able to fix the problem with the black squares around the 2D sprites in the game. However, the screenshots on project's website show, that this could be some specific problem with my hardware. If you find any solution for this problem, please contact me by mail or leave a comment to this article.