Continuity mistake: When Ms. Dubcek is showing the Solomons the attic apartment in the pilot episode, they enter (and she later exits) through what is Dick's bedroom in all subsequent episodes. Additionally the staircase at the back of the living room that serves as an entry point is completely missing.
Visible crew/equipment: When Dick wants to go along with Mary to a wedding he tries to convince her. When he says "Whatever it takes, I'll do it" he walks forward. Take a look at the top of the screen and you'll notice the shadow of the boom mic on the wall following him.