There is one bug which is OpenAL specific, I think, dealing with mono 16-bit sound files. They have static in them and it only happens with streaming sound (voices). Converting the same files to 8-bit PCM, OGG or MS-ADPCM will result in them working fine. I haven't figured that problem out yet, but it's not really a TBP specific thing either.
As a primary Linux user/developer and avid Babylon 5 fan I have no problems supporting Linux/TBP stuff. If it's broken, and an actual code problem, you can be damn sure that it will get fixed pretty quickly. I've been playing 3.2 (RW 2.0) for the past few days nearly non-stop in fact. Other than a few problems which would affect Windows as well (mainly hitting Assert()'s and Int3()'s from mission problems) the only real problem with TBP is that it requires Windows to actually install. That's the only thing that sucks right now as a Linux user. It's a pretty good bet Linux users are going to be B5 fans but your installer is a pretty big turn off for that crowd. And the FS2 Linux community is quite a bit bigger than you would think too. I would say that only about 5% of the FS2 Linux users I know of actually post in these forums. When 3.6.7 actually goes official, FS2_Open will even end up in a Linux distro or two apparently so the user base could nearly double from that.
Regarding bugs, the big problems seem to mostly be graphics related at the moment. The Linux version is quite a few steps ahead here since it doesn't support D3D and all drivers focus on OGL support. The Linux specific code has been well tested and optimized over the past few years so pretty much every bug that the Linux version sees are bugs that hurt the Windows version as well. There is the ocasional exception but with me using Linux almost exclusively and WMCoolmon getting into it more and more and two, possibly three, of the other developers are at least playing with Linux. And quite a few of the better bug reporters/fixers who aren't official developers use Linux too.
Holy crap! I just realized that I sound like one of those freaky Linux advocates!
I'm not doing the whole GNU/Linux thing yet though so maybe there is still hope for me.