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.
Never Meet Your Heroes - S1-E1
Continuity mistake: The little girl is barefoot in the opening scenes but when her feet are reflected on the oven door she has white socks on.
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.
Episode #1.1 - S1-E1
Continuity mistake: When Mark got into his cell, the top bunk had a vinyl-like covered mattress (or folded gym mat) that had a lengthwise seam along the middle of the side. He was not fixing his bunk bed while he was talking to cellmate Bernard, but when he was removing items from his bag on top of the bunk bed, it was now covered with a blue blanket and a sheet folded down by the pillow could be seen. A little later, the blanket was also covering the foot of the bed. (00:13:15 - 00:15:03)
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)
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)
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)