Hi, I'm the user "Princess" on the NSF site and I've mainly been involved with cleaning up the file at the TS level. I can answer any questions you like.
The best summary for the Slashdot audience would be this one
by Lourens, it explains things simply without dumbing things down.
The types of problems we have are basically that bits have been either flipped or (rarely) omitted. The flips tend to clump together, i.e. you'll get an area that's good and then an area that's awful.
The work is approximately divided into two parts: fixing up the file, and fixing up the video that results. I work on fixing the file, and from that I can find extra frames and pieces of MPEG4 data for the video people. Fixing the video is done by using a modified version of ffmpeg that can change macroblock pointers, ordering, luma and chroma. This work is not done on the file directly and can't easily be mapped back to the file, so it's not just a question of flipping bits once you get to the video level.
Other technical info: The video itself is a broadcast (fixed bandwidth) MPEG-TS stream containing one video stream, a 704x480 MPEG4 stream at approx. 15 fps (technically half the NTSC framerate which is 15000 / 1001 fps).