Continuity mistake: When Hannah makes the list with names involving her past events, they differ substantially between the close-up when they're written and the final wide angle once the paper is finished. Check Alexander: first an irregular oval with a straight side, then a perfect oval.
Continuity mistake: When we see Hannah in the room (when Bryce and Justin are talking about beer pong and stuff before Bryce walks in), the door stays shut the whole time. But when the camera shows Bryce's side, the door opens slightly, but Justin closes it.
Continuity mistake: During the first tape Hannah says that there are 13 tapes as there are 13 sides to every story, however we later find out that she only planned and recorded 12 tapes that night, and the 13th (Mr Porter's) was unplanned and recorded later on, so she would not have included it with the others when she mentioned how many tapes she was going to make in the beginning.
Continuity mistake: At the end of the episode, the scenery outside Tony's window changes. We first see a body of water and grass, which then changes to a row of houses, grass, and a smaller body of water in the big overhead shot.