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.
Reptile Boy - S2-E5
Continuity mistake: When Buffy is at the party, we see that she is wearing black shoes with a high heel. But when she is fighting Machida, the heels are considerably lower.
School Hard - S2-E3
Plot hole: When Buffy and Sheila are walking out of school after the meeting with Snyder, Xander runs up to talk to them. He mentions during this scene how Buffy will be helping out at the Parent-Teacher Night, but he shouldn't know this - Buffy only just found out about it in the meeting with Snyder.
Revealing mistake: Throughout almost the entire sword fight between Buffy and Angel, from the far away shots, its clear that the actors are stunt doubles. It's very visible when there is a shot from the top. (00:34:05)
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)
Some Assembly Required - S2-E2
Visible crew/equipment: As Buffy goes through the door with the "Keep Out" sign on it, the shadow of a camera can be seen on the left side of the door in the last few frames of the shot.
Other mistake: At the end of the episode Willow mentions going to the Bronze on a Wednesday night, Buffy also mentions to Giles that she got almost everyone killed on the second day of school. From the different clothing being worn each day, it's obviously been more than 2 school days and should instead be Thursday by the end of the episode.
Continuity mistake: When Willow is interrogating Jonathan, she makes a comment about how he resented being pushed around. In the first shot, she's facing him. It then cuts to the opposite angle, and she's facing sideways. Then, in the very next shot, she suddenly turns 180 degrees between cuts after walking by him.
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.
Audio problem: Jenny prints off the translation for the Ritual of Restoration from her computer, then spots Angel sitting across the room from her. As she gets up and starts walking towards him the sound of the printer can be heard but the paper has already finished printing.
Plot hole: In the flashback to Buffy in L.A., how did Angel get there with the front windshield of his car blacked out? Being a vampire, he obviously needs it during the day, but he also wouldn't be able to see traffic. And it just seems to be too much of hassle for him to remove it at sunset, just to reapply it at sunrise, just to remove it again, etc.
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.
Revealing mistake: When Buffy and Angel are sword-fighting, the camera pans up and to the side, you can see David Boreanaz's stunt double. His hair line is farther back then David Boreanaz's.
Visible crew/equipment: When Ampata agrees to go to the dance with Xander and they walk off down the hall, a shoe can be seen in the bottom right of the screen within the last few frames stepping into shot.
I Only Have Eyes For You - S2-E19
Continuity mistake: When George shoots Mrs. Frank, her body falls off the balcony headfirst on a closeup shot. She flips in the air once on her way down. But in the following wide shot, she flips in the air on her way down again.
Other mistake: In the basement when Death throws Ryan to the floor, Ryan lands pretty softly considering that he was just thrown pretty hard.
Some Assembly Required - S2-E2
Continuity mistake: When Cordelia is being tied up in the corridor, Buffy leaps up, kicks the attacker, and drops to the ground next to Cordelia. In the next shot the attacker is stumbling to his feet, and Buffy is standing again, then quickly kneels down beside Cordy.
Revealing mistake: When Buffy is fighting the vampires that are trying to resurrect The Master, at one point she is grabbed from behind by a male vampire and kicks a female vampire in a green top twice (right after Absalom shouts "The sacrifices! Stop them!"). If you watch closely, both of the kicks miss the vampire, revealing that the fight was choreographed. The punch that she delivers to the male vampire afterwards also looks fake.
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.