Deliberate mistake: When James is shot on the courthouse steps, the crowd of reporters that has gathered quickly scatters to escape the gunfire. One of them is a woman in a black windbreaker holding a camera. The camera cuts away briefly and then back to the crowd - you see the exact same people, including the woman in black running in the exact opposite direction as before. The footage was apparently mirrored and repeated for the second shot of the fleeing crowd.
Factual error: The scene where Pierson Bartlett is on the stand, he pulls a spoon out of his jacket. This would never be allowed. He wouldn't get through the metal detector with any metal that could be used as a weapon. He would either have to take it back to his car, or leave it at the security desk.
Other mistake: An ambulance, when Kathy Stabler gives birth to the baby, Olivia says the baby's a girl. In the hospital, when Elliot gets to Kathy's table's room, she tells him the baby's a boy.
Suggested correction: Olivia never says the baby's a girl. Rewatch, please. In the ambulance, when Kathy is in the midst of the last few pushes to get the baby out, Olivia is watching the delivery over Kathy's shoulder, being supportive. With Kathy's last push, Olivia repeats, "Good girl, good girl," which is directed at Kathy to encourage her pushing during her delivery (timecode 00:39:20). Then, when the baby is out, Olivia excitedly exclaims, "It's a boy!"
Visible crew/equipment: After Picard headbutts Stabler into the car window and runs away, Benson runs over to comfort him. As she cradles him, the reflection in the side of the car shows the camera person filming as the shot gets closer. (00:14:05)
Visible crew/equipment: As Stabler is bringing Saul Picard to the cop car after finding him in the park, a large boom mic is visible in the reflection of the car's window as Stabler opens the door. (00:13:40)