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 the living-doll version of Glen/Glenda/GG is revealed, after they thank Tiffany for giving them a makeover, the way they are holding the mirror changes instantly between cuts. This then continues throughout the rest of the scene, with them holding the mirror in a different way between shots probably a dozen times.
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.
