I'm not going to go into episode-by-episode detail as for the first season. Too many comments would be spoilers, and I'm gearing up for Marscon.
Season 2 is much, MUCH better than season 1, which was awful (with a few good moments). A major caveat: Season 1 was short, 12 episodes, and while it has a Season Ending Show, all the weaknesses of the first season spill over into the first four shows of season 2. Fortunately for the casual viewer wanting to catch up, that means you can ignore the first disk of the six-disk set.
The episodes get much better, fairly quickly, starting with Serpent Boy. Interestingly enough (for me), I watched a broadcast of that show. I only remember because while it wasn't enough to make me a regular viewer, a line from the show made my quotefile. Willow to Angel: "You! You're going to live forever. You don't have time for a cup of coffee?"
The major improvement is in the writing. The special effects are still cheesy, the lighting far too dark, Sarah Michelle Gellar isn't a particularly good actress. Still, she's really good at pouting, and she frowns her way through the second season and finally gets to chew the scenery (and do her own sword-play) in the final episode. Everyone's character gets fleshed out well, and the supporting cast carries the day. Joss Wheadon figures out how to make a show about people, rather than a one-joke show with a gimmick every episode.
A mini-essay on why the "High School As Metaphor For Hell" doesn't work for me, even though I hated HS as much as anyone, is too much for the present. Xander is clearly the character closest to my own experience (and not very close at that), so it was nice to see him get some juicy lines, get the girl and get confident.
The extras on the DVDs are no better than okay: only two commentaries, iirc, an interview with Whedon broken up into bits and scattered among the relevant episodes, some featurettes on the last CD.
I almost gave up after the first season, but enough LJ Friends convinced me to plug through the second season. Thanks for the recommendation, and thanks for not spoiling the story arc. I'm looking forward to Season 3.
Between Buffy 1 & 2, I cleansed my palate with Mission: Impossible, and am still working my way through the first season, before Jim Phelps arrived. It doesn't really hold up, but it's nice to see so many Star Trek personnel in other roles. (ST and MI were made by the same production company, Desilu.) On the other hand, MI is a full 50 minutes (vs. Buffy's 44), and a season was 28 episodes (vs. 22 max). Ah, the good ol' days, when we had to walk uphill both ways and the tv set was black and white BUT there were fewer commercials and more show.