Revealing mistake: In the beginning of the episode, when Buffy stakes the vampire that she beats up for a long time, watch when she lifts the stake. The hole in the vampire's chest is a solid 8" below where she actually hit him with the stake. (It's an effects shot, so somehow, they just didn't line up).
Continuity mistake: Right as Buffy gets out of the car and watches Joyce drive away, Cordelia and her friend are walking up the stairs, along with a girl in a blue shirt at the top of the stairs walking towards the school. The next shot Buffy is walking towards the stairs, Cordelia is already far away chatting with her friend and the girl is blue is back on the stairs again. (00:27:00)
Continuity mistake: After drinking the water with the virus, Buffy looks into a room and her hair is damp and brushed back. In the next shot, it's dry and parted down the middle.
Other mistake: Buffy freaks out when she's first taken to the hospital. Joyce tells the gang it was because her cousin died when they were young, but in season one episode "Angel" Buffy has no problem being in the hospital, same with later seasons.
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.