Well the most obvious way and least elegant way to do the replay feature, would be to have the physics engine dump the location data (x,y,z,facing, type of object) of all objects in the game at a set interval. The challenge would then be to get this data back into the engine in a fashion that would allow for the user to control the playback the replay.
if you are going to do that how about writing to a variation on a mission file? then it would be viewable in the techroom.
I don't see how a writing it as a variation of a mission file is going to help, but the viewer system certainly could (should) be accessible in the techroom. I really don't know how else we would setup access to it anyway. I guess we could use a commandline flag to start FSO straight into a recorded mission, either from the players perspective or an arbitrary ships perspective.
the other option would be to record the display and audio output to a file then run a convertor into a popular video file
Ya, but this would not allow the replay to have the omnipotent camera that was being discussed, you are stuck with what the player seen when they played. This would be no different than what we can accomplish now with x-fire or FRAPS.
How about an incomplete demo recording system?
IIRC there's one of those lurking in the code somewhere too. 
That is essentially what we are looking for, while allowing the user to control the camera.