The missing bit in Tholian Web was in sickbay as McCoy was releasing Uhura. They cut off the last part of that.
Yup, The Menagerie part 2 had music replaced weirdly, only for the fade-ins. At the start of the episode, a re-recording from the Fred Steiner LP from 1985 was used. The episode titles used Doomsday Machine music. Act 2 had more music from the LP. No idea why this was done, or why it was never corrected. The music could have been taken from any number of sources if the original sources were damaged. As I said, the mono broadcast track on the BD has the oringal music. So do the VHS tapes and Laserdiscs. I've made the replacement myself on my consumer video program and it took minutes. Go figure.