Hmm, cool topic!
Agreed, it's been said before but yea, Jesse's death was gotten over way to quickly. Maybe a Xander focused episode where his hatred for Angel is linked to his hate for vampires because they killed his best friend.
I think it would have been cool to deepen the relationship between Buffy and Giles more. Maybe an episode where for some reason they had to rely soley on each other to escape, without the aid of Jenny, Willow, Angel, or Xander. More of just watcher/slayer.
Also, it would have been cool to have had more Jenny in there. Maybe have had Giles and Jenny date and get together before the end of season 1, maybe even have had her become a regular cast member by season 2. I think that it would have made the reveal of her being sent to watch Angel have even more of an impact because the audience would have had more invested in her as main character.
And I would have loved some more backstory on Willow and Xander and their frienship before Buffy. So maybe an episode where the focus is more on them with some flashbacks and such. Season 1 was good at laying the groundwork for the series and a little more backstory on Willow and Xander would have been fun!