I quickly smashed together a video.
http://www.youtube.com/watch?v=xANvyzcIJBE
(This video is poorly made, no editing or anything of the sort and very poor compression so I could upload quickly)
The problem occurs on any moving platforms. They all seem to act weird when I am on them and they're moving at the same time. Skip to 15-19 seconds in the video to see the problem if you're impatient. The code has virtually nothing changed and is really only ported to C++ at this point and partially OO. I don't see how that could break anything like that, though. Nothing else appears to be broken, other than me getting snagged/stuck on inclines quite often.
Note: This doesn't happen in multi-player.
Any ideas of what the problem could be? The code is based on Fitzquake.