Episode #1.6 - S1-E6
Continuity mistake: Sami takes Maya directly from the location where Tommy Dark's body is found to his home, but Maya's outfit is completely different when they arrive.
Family Tree - S1-E3
Continuity mistake: When John goes to Per's home to convince him to return to work, John's shirt, which is initially hidden under his sweater, becomes visible as they walk.
Character mistake: Elliot is sitting on the porch with his mother. He says dizziness could be a sign of a heart attack, or a cardiac spasm that could lead to a myocardial infarction. Elliot is an exceptionally well-informed kid who would know that a myocardial infarction is a heart attack.
And in the Beginning... - S1-E1
Factual error: The show is set in 1991, and Dexter walks past a Lehman Brothers stall at the jobs fair. The problem is that the stall and the marketing materials on it have the modern-day Lehman Brothers logo and branding. Back in 1991, the bank was called Shearson Lehman Brothers and had a completely different logo and colour scheme. It was only spun off into Lehman Brothers in 1994. (00:10:03)
Episode #1.4 - S1-E4
Continuity mistake: DC Li is wearing a white crewneck sweater with a blue band on the neckline until this episode, when she is suddenly wearing a blue button-up shirt. All episodes take place on a single flight.