Revealing mistake: Drusilla's reflection can be seen in the metal part of what appears to be the base of a shopping mall map just as she's getting up after the Judge has been blown up.
Continuity mistake: When Buffy is told that Angel has become Angelus, she mentions "I should have known. When I saw him at the house he was different", but her earlier conversation with him took place not at the house but at his apartment. This isn't just a strange turn of phrase - the scene was originally shot at the Summers house, but was changed to Angel's apartment for more emotional resonance.
Plot hole: After losing his soul, Angelus kills Jenny Calender's uncle, who is a descendant of the gypsy clan who cursed him. But, since there is nothing to suggest the uncle's room is in a public location, Angelus couldn't have gotten in the room without an invitation.
Visible crew/equipment: Right after Kane and Buffy's fight in the woods, in the shot right after Kane leaves, you can see set-lights above the clearing where they fought. (00:39:10)
Continuity mistake: When Willow shows up at Oz's house to talk, her hair keeps switching back and forth between being behind her back or in front of her shoulders.
Bewitched, Bothered And Bewildered - S2-E16
Other mistake: Joyce tells Cordelia to grab some bandages for Xander from the bathroom upstairs. Joyce and Xander are in the kitchen and there is a small corridor that leads to the stairs, but Cordelia goes around the other way leading to the living room. Fair enough, Cordelia made a mistake. She isn't that bright. But she returns with the bandages coming back from the living room. Why come downstairs and then go All The Way around through the living room when she could have just walked down the small corridor?
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).
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)
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.
Other mistake: In the basement when Death throws Ryan to the floor, Ryan lands pretty softly considering that he was just thrown pretty hard.
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.
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.
I Only Have Eyes For You - S2-E19
Visible crew/equipment: When Xander opens his locker and the gross hand grabs him, if you use slow-mo when the shot is inside the locker looking out, you can see the white t-shirt of the man whose arm it is. (00:10:20)
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)
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.