You know, it's interesting. I don't think it was so much that the show itself was actually dated because, in season two, the show seemed to get a whole new look, especially in the way the students dressed. It felt more normal, I guess. Season 2 felt a lot like later seasons.
I think, mainly, season one was going for a certain appearance. Also, I think the first season was kinda supposed to look like what Buffy, the movie looked like, which was done in the early '90's, I believe. I mean, we have the extremes. The geeky Willow with her long dresses and stockings, we've got the fashionable Buffy in her short skirts and make-up and nail polish and we've got Xander who's supposed to be "the average guy". I mean, going through high school I don't ever remember girls wearing skirts that short to school or wearing dresses all the time (or if at all, really). Okay, so I was in high school in '98, not '96 but still. I don't think styles change that much in only a year or two.
So for season 1, I think it was all about getting a certain image across as far as the show was concerned. I don't know how much it really reflected on the average styles of that time. Because in season 2, I think you definitely see a shift in the way people look. Buffy, for one, I don't remember her wearing as much make-up as she did in season 1 and Willow was out of her long dresses and stockings.