Continuity mistake: Willow is turned into a ghost. Throughout the entire episode, she can't touch anything (can't turn the pages of a book, etc.), yet towards the end when she and Giles go to Ethan's shop, and she leaves, you can hear that she opened and closed the door, even though she can walk through walls and can't actually touch the door. The curtain moves when she leaves too. (00:34:05)
I Only Have Eyes For You - S2-E19
Factual error: In the episode 'I Only Have Eyes For You', during the flashbacks to 1955 James and Grace dance, and James later shoots himself, to the song 'I Only Have Eyes For You', which wasn't released until 1959. (00:18:20 - 00:26:50)
Continuity mistake: While Buffy is in the hospital, they zoom in on the bedside clock changing from 2:26 to 2:27. In the next shot of Buffy, you can see the clock in the background and it reads 12:15.
Continuity mistake: Joyce is driving Buffy to school and she is wearing a pink tank top. At school that day her shirt is white, but the next day at school she is back to wearing the pink outfit. (00:15:50)
I Only Have Eyes For You - S2-E19
Visible crew/equipment: After the history teacher writes, "Don't walk away from me, bitch!" on the chalk board, Buffy says to Xander, "I'm telling you, something weird is going on." As she says "something", a boom mic is reflected in the window behind her on the right.
School Hard - S2-E3
Continuity mistake: When Spike appears at the Bronze and lures Buffy outside, she runs past her table which has her jacket on it. But once she is outside she suddenly has her jacket on.
Continuity mistake: When Buffy is fighting Kendra the fragments of the table she is thrown onto have disappeared when she stands up again. (00:42:40)
Continuity mistake: The white outline drawn by the coroner does not match where Kendra's body fell after being killed by Drusilla.
Other mistake: When Angel, Drusilla and The Judge enter the mall, The Judge kills a pedestrian as he tries to get away. But no other pedestrians that are in the mall notice - A big blue guy just set a man on fire and disintegrated him into tiny pieces in a public mall and NOBODY noticed?
Continuity mistake: When Buffy looks into the childrens' ward the sign on the door saying 'Basement Access' disappears and reappears between shots. (00:12:00 - 00:36:15)
Deliberate mistake: After Jenny pushes the janitor's cart into Angelus and runs up the stairs, there's no physical way he could be waiting for her at the top of the stairs (even with vampiric speed). Joss Whedon has admitted in interviews that he put in this blatant continuity error as the situation is a staple of the horror genre (girl runs from villain, only to find him standing right in front of her).
School Hard - S2-E3
Continuity mistake: While studying at the Bronze, Buffy and Willow leave their books on the table to go and dance. Spike calls them outside to fight a vampire, and when Xander runs back inside to grab a stake the books have all been put back into Buffy's bag. (00:14:00 - 00:15:45)
Audio problem: When Xander, Willow and Ampata meet up at The Bronze, the song the band is playing is at the point of a guitar solo. If you watch Oz (who has already been established as 'lead guitarist') on stage in the background; he's blatantly NOT playing that solo. The hand movements don't match up.
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.