Revealing mistake: Several times during Spike's escape from The Initiative, his reflection can be seen in the glass. Vampires aren't supposed to have reflections. (00:13:00)
Visible crew/equipment: In the scene where Spike escapes from The Initiative a black curtain can be seen to the right of the screen after the other vampire is release from his cell. The curtain serves no purpose to the set or scene and it disappears in the next shot. (00:13:25)
Factual error: In "The Initiative," Riley is looking for Spike with a heat sensitive camera and says "we've got a cold one." If Spike was at room temperature as indicated on the sensor, he would be indistinguishable from from the air and objects in the room. (00:37:30)
Continuity mistake: In 'The Initiative', Riley, Graham and Forrest are looking in through the windows of Stevenson Hall with thermal goggles looking for Spike, they see him walking towards Willow. When we see Willow and Spike seconds later he is still sitting on the bed where he was for most of the scene. (00:37:30)
Plot hole: Spike must have had his chip implanted while he was unconcious. If so, how did he attack The Initiative scientists without any pain when he tried to escape? You could argue that they programmed him to be capable of violence within The Initiative only, but why would super smart scientists program an evil being to be able to escape at the first opportunity? Joss Whedon has acknowledged this as an oversight.
Continuity mistake: At the party where Riley is talking to Buffy by the stairs, when he first comes over there is no one in the corner on the stairs but in the next shot there are two people who disappear two shots later.
Character mistake: At Riley's party, Willow tells him that Buffy is wearing a halter top when she is in fact wearing a strappy top. Being a girl, and extremely into fashion at this stage in her life after her high school years, she should have known better.
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.