Episode #1.4 - S1-E4
Continuity mistake: The captain of the submarine has the rank of Commander (3 solid stripes) and half-way through episode 4 the captain suddenly has the rank of Captain (4 solid stripes) as shown on his shoulder epaulettes.
True Crime - S1-E1
Continuity mistake: When we're introduced to Oliver, the people walking by behind him appear / disappear / reappear randomly with no continuity whatsoever.
The Digital Frankenstein Job - S3-E2
Continuity mistake: When the panicked CEO is in the diner holding up a printed gun, saying "I make these," in shots from behind his fingers on the trigger, but in shots from the front he's just holding the grip. (00:40:10)
Continuity mistake: Mare and the Chief of Police are outside talking in the rain under umbrellas. They put away their umbrellas, although there is still the sound of rain, but neither Mare nor the Chief of Police is getting wet. (00:54:37 - 00:57:07)
Planes, Trains, and Automobiles - S2-E1
Continuity mistake: S2/E1 Planes, Trains, and Automobiles: Ashley smoked her cigarette down to the filter with no white cigarette showing but in the next frame there's white cigarette showing. (00:11:23)
Episode #1.1 - S1-E1
Continuity mistake: The night Bernard got back to the cell, a view inside is backwards - the bed is on the opposite side of the window, followed by a close-up shot of Mark sleeping with the bed on the right side. (00:41:31 - 00:43:56)
Continuity mistake: When Kate goes to see the LARPers at the park to track down the trick arrows, her cross-body leather strap changes direction repeatedly. At first, it hangs from Kate's right shoulder to her left hip, but when Kate asks about the cop in their group, the strap hangs from her left shoulder. Then the leather strap reverts to the original way, only to switch yet again after the fist bump. None of the shots are flipped. (00:20:10)
The Outlaw Eddie Wagner - S2-E3
Continuity mistake: Stabler is patted down by a NYPD Officer and the officer is shown slipping something into Stabler's left front pants pocket. After the officer departs Stabler pulls a paper out of his front right pants pocket. (00:15:52 - 00:16:30)
Episode #1.7 - S1-E7
Continuity mistake: Monique is making "tea" for Stephanie. She is stirring the drink and suddenly the glass is way more empty. (00:25:13)