Continuity mistake: In the episode Prophecy Girl, during Buffy's rooftop fight with the Master, her shoes change in between shots from white heels, to black boots when she's kicking him, back to white heels. (00:41:35)
Continuity mistake: When Buffy drowns in Prophecy Girl, she falls into the pool with her hair tied in a ponytail and her arms under her. When she is discovered by Angel and Xander, her arms are by her sides and her hair is loose. (00:33:55)
Continuity mistake: When Buffy falls down after the Master bites her, you can see her fall, then hear her hit the dry ground. But then a few shots later she falls again and this time into water.
Other mistake: The Master's skeleton, before it is destroyed, looks to be female and not male. (Note the wide hips and large birth canal-like hole.) Also in the Next season's "When She Was Bad," they have another shot of the same skeleton, however the hips are much smaller and more male. (00:43:55)
Audio problem: When Willow and Jenny jump in Cordy's car, Cordy mentions that she saw "these things coming at me!" However, her mouth isn't moving for the last few words.
Deliberate mistake: When Willow and Jenny go out to the parking lot only to discover vampires converging on the school, pay attention to the extras. You can make out some of the same extras in different shots coming from different directions. (Most notably, you can see a woman in a long black-and-white skirt coming from the direction of the parking lot, then a few shots later, she's suddenly over in the football field coming from there.) They obviously reused extras in different shots to "pad out" the crowds.
Continuity mistake: When Buffy descends into the Master's lair, the way she is holding her crossbow changes depending on the camera angle. Sometimes it's pointed straight forward, sometimes it's pointed upwards.
Continuity mistake: When Giles and Jenny are talking about Buffy, Giles says "We must get in touch with this Brother Luca chap!" watch Giles. In the first shot he's still reaching towards the top of the cabinet. Instantly in the next shot, he's in the middle pulling something down from the top of the cabinet.
Continuity mistake: When Giles and Jenny are talking in the library, when Jenny closes the bible, the way she's holding it changes instantly between shots.
Continuity mistake: When Buffy is consoling Willow after she discovered the dead students, as Buffy leaves the room, Willow's mouth is open and she looks down. It then cuts to a wideshot. Instantly, Willow's mouth is closed and she's staring forward, and she looks down a second time.
Continuity mistake: When Jenny meets Giles after Xander's botched attempt at asking out Buffy, the way she's holding the folders to her chest subtly changes repeatedly between the closeup and wide shots.
Continuity mistake: When Buffy turns down Xander's date proposal at the start of the episode, throughout the scene, Xander has his backpack up around his right shoulder. However, when he walks away, it's instantly down by his side.
Visible crew/equipment: When Buffy meets Giles in the library after the opening credits, and they start talking, throughout the scene, you can see set lights and reflectors reflected in Giles' glasses multiple times. This happens often throughout the series, but is particularly noticeable here.
Revealing mistake: When Willow says "The usual " at the beginning of the episode and it cuts to Buffy landing on the ground, you can briefly but see the stunt woman playing Buffy's face in the first shot for a solid second or two. That definitely isn't Sarah Michelle Gellar.
Continuity mistake: In the beginning, when Xander is practicing asking Buffy out with Willow, at once point Willow puts one of her snacks (candies, I think) into her mouth and starts chewing in a medium/wide profile shot of the two. It then cuts to a closeup of her and instantly she's no longer chewing, and immediately places a second candy in her mouth. She didn't have time to stop chewing and swallow between cuts.
Continuity mistake: When the earthquake happens at the start of the episode, and we see the Master celebrating, his hands instantly change positions at least twice between cuts. (Sometimes it matches perfectly between cuts other times they're in an entirely different position between cuts).
Continuity mistake: When Buffy stakes the first vampire at the beginning, in the first shot, his hands are in towards his abdomen. When the camera cuts behind him, and he falls back, suddenly they're instantly extended partially outwards to either side.
Continuity mistake: When Cordy stops kissing her boyfriend and says "What was that?" at the beginning of the episode, the lighting on Cordy's face changes completely as it cuts between the two camera angles. In the first angle, the lighting is much darker and shadowy, while in the second angle, her face is suddenly much brighter.
Plot hole: Angel says he cannot give Buffy mouth-to-mouth because vampires have "no breath." However, throughout the entire series, vampires are shown to breathe, and are able to do things like smoke, gasp, get choked out, etc. (Granted, the franchise also confirms a vampire cannot die from asphyxiation, but still they're shown to breathe regularly).
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.