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.