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.
Continuity mistake: When Jake walks away at the beginning of the episode and the homeowner notices the butcher knife is gone, the way she has her hands resting on the moneybox changes between cuts.
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)
Family Day - S2-E5
Continuity mistake: When Harry first picks up a water balloon and throws it, his hands are now empty. In the next shot, he has a blue water balloon in his hand. When he throws that one, you see it's a pink balloon being thrown.
