Continuity mistake: When the video of Kimmy plays on the school announcements, and she talks about Duncan being hung up on Veronica, there is a cut to Duncan reacting with raised eyebrows in the foreground, while Veronica can be seen in the background with a passive expression. Then it cuts to a close-up of Veronica having a visible reaction with her whole face falling. But since Veronica and Duncan were reacting to the same thing, Veronica's reaction should have been visible in the first shot as well.
Continuity mistake: Deputy Leo is at the police station when a woman reports her daughter is missing, but moments later when Keith tracks Veronica to a storage/warehouse, Leo is playing with his band and doesn't seem to know what is going on and Keith has to tell him that a girl is kidnapped.
Credit Where Credit's Due - S1-E2
Continuity mistake: During the diner scene with Keith, Veronica and Lamb, Lamb leaves and Veronica starts to go next. As Veronica starts to leave, still sitting in the booth, she puts on her hat (right after she says to Lamb "smell ya later"). The camera angle is on Keith, but you can barely see Veronica putting on her hat. In the next shot, the angle is on Veronica who is just packing up her books. She has no hat on, but then puts it on (again).
Continuity mistake: At the end of the episode, Veronica knocks on the door of room 6, implying that it was empty. In the next shot, we see under the sign for The Camelot, it says "No Vacancies" meaning Lianne could possibly be there still.
Continuity mistake: When Veronica shows Keith the picture of Rain on the milk carton, she turns the carton around and tilts it backwards with her hand. In the next shot, her hand has disappeared and the carton is sitting flat on the table top. (00:33:25)
Continuity mistake: The morning after Veronica is raped, she readjusts her dress' strap on her left shoulder. In the immediate shot after, the strap is down again. (00:22:00)