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.
Factual error: At the very start, the lead parachutist says they're jumping from 30,000 feet, the altimeter confirms it, everyone whoops and cheers, and he gets them to put their masks on just before jumping. Two problems - the plane they're in is a De Havilland DHC-6 Twin Otter with a maximum altitude of 25,000 feet. And at 30,000 feet in an unpressurised aircraft there'd be nowhere near enough oxygen for shouting and cheering - they all should have had their masks on already.
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.
Plot hole: This series depicts Dexter and Harry working together at Miami Metro. However, the original series established that Harry died before Dexter ever started working at Miami Metro.
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.