Other mistake: When Sid gets into Buffy's bed and Buffy screams, her mum immediately comes into her room to find out what's wrong. Now, unless she sleeps on the landing, Buffy's mum is really quick at getting out of bed.
Other mistake: In the very first shot (a long tracking shot backstage), watch the girl practising with her tuba. At one point she pulls her mouth away and then leans back in and starts playing some notes. But you can tell that she isn't blowing into it, and in fact, her mouth isn't even quite touching it. So it shouldn't be producing any notes. Then, almost immediately after, you can also see the actress purposely moving the tuba (sort-of rotating it to her right) to get out of the cameraman's way.
Chosen answer: Angel is saying that he is still jealous and Buffy recognizes that this is his way of saying he wishes that they could be together. That is why they both smile.