I also rewatched The Three Doctors
recently in preparation for the special because it's the first multi-Doctor story and was also made to celebrate an anniversary (the 10th).
It's a bit silly but I love the interaction between Two and Three, the eccentric supporting characters, the Brig being himself and the First Doctor's line about the Dandy and the Clown.
I like the ending a lot, too. The Doctor finally gets his ability to time travel back but decides to stick around a bit with UNIT, anyway - a marked contrast to his first season where he tried to get away whenever the opportunity seemingly presented itself.