Continuity mistake: When Jasmine picks up the car and throws it at Angel, it cuts to a shot of Angel moving out of the way then shows the car falling from the bridge. First mistake, Jasmine disappears from the shot when the car is falling, and second, the car falls directly straight and at a higher point than Jasmine actually threw it. (00:35:50)
Other mistake: The Chinese writing shown tattooed all over Wo-Pang's body is nonsense (a small number of random characters repeatedly jumbled together), although Wesley reads it as if it is language. (Although one might argue that the writing is meant to be some sort of code, there is no evidence in the show itself to suggest that, and Wesley refers to "translating" rather than "decoding" it; for these reasons it is more likely to be simply a mistake rather than an intentional decision.) (00:16:40)
Revealing mistake: At the vampires' nest, when Knox is talking about Gunn's team, the vampire wearing the green sweatshirt and leather vest doesn't have yellow eyes like the other vampires do. And the female vampire doesn't either later, when the two groups face off after Gunn's sister is sired. (00:22:30 - 00:35:35)
Character mistake: While Gunn and Lorne are interrogating Framkin he sings a couple bars of a song "Courage and Pluck". However, though he has the ability to read people when they sing, and in fact in the very next episode knows that Fred is about to fall from just the words "you make me happy", Lorne doesn't read him.
Continuity mistake: When the demon Angel and Groo are chasing crashes through a wall, the resulting hole lets in enough sunlight to force Angel into the shadows. A few shots later, Wesley notices Angel standing in the entrance to the hole. Only a few moments have passed, so Angel shouldn't be able to stand where he is. (00:15:20 - 00:16:20)