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.
Give Me Something Good to Eat - S1-E2
Continuity mistake: When Jake tells Junior to call 911, Junior sets down a magazine. In the next shot, you can just barely see that there's suddenly some pamphlets on top of the magazine, even though it should be on top of them.
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.