ZeqMacaw and I have been working on a wrapper for the Direct3D part of Jedi Knight. Zeq gave me a build of it this morning that fixes the awful HOM-like artifacts that most people see with newer video cards when using 3D acceleration.
I did some initial research into the problem but Zeq has done most of the work to make it happen, so credit goes to him.
Basically, there's a function called in DX5 that is broken on newer video drivers. The fix is a wrapper for ddraw.dll that wraps calls from DirectX to DirectX 7, where a different, non-broken function can be called. Once a full wrapper is implemented, we should be able to add other, minor graphical features to JK. So essentially it is a replacement ddraw.dll file that goes in your JK directory. Should work with the Steam versions, too.
I don't know the status of the fix so I haven't uploaded it, but something should be available soon.