Visible crew/equipment: When Claire runs away from Bob after he calls her "Ms. Bennet", you can see Bob's shadow and another person's shadow on the ground. Since no one else was standing next to them, it has to be a crew member, most likely a camera man based on the odd shape of the shadow.
Continuity mistake: The door to Dexter's apartment opens out toward the walkway. However, in all subsequent episodes the door opens into his apartment.
Bargaining - S1-E5
Continuity mistake: When the guy at the restaurant dies he falls behind the broom, but an instant later he is in front of it.
In Too Deep - S1-E23
Continuity mistake: When Ms. Chatham is at Emma's house, she puts her hand on Cleo's arm. It's not there in the next shot. (00:10:35)
Factual error: Gay pride flags are visible in a window. The 6 color flags shown were introduced in 1979 (though an 8 color flag preceded it in 1978). (00:30:44)
Suggested correction: Ms. Chatham's hand is barely visible in the next shot but it's there.
The fact that it's barely visible (as seen in the screenshot) confirms the mistake. It's on her arm and then it's not on it, she's just barely touching.
Bishop73