Visible crew/equipment: In the shoot 'em up scene at the hangar near the beginning of the film, right after Tito and Wanda take down Pollux, when Troy shoots an agent in the stomach and the agent flies back - you can see at least two cable wires pulling him backwards. You can first notice the 2 wires when the agent is running in slow motion right before he shoots him. (00:14:15)
Visible crew/equipment: At the L.A. Convention Center, just before Castor Troy (as Sean Archer) disarms the bomb, there are a few shots of all the extras evacuating the area. In the interior shot, that looks out through the glass doors onto the street, the tracking crane arm with a seated camera operator and camera on its platform is visible as it shoots an exterior crane shot of all the extras, which was seen among the previous shots.
Visible crew/equipment: When Sean first visits the Walsh Institute, he, Dr. Miller and Dr. Walsh walk in front of the circular glass window to view the ear reconstruction. In the next shot facing them, the reflection of a boom operator holding the boom pole is visible on the glass in front of Dr. Miller and Sean. (00:24:50)
Other mistake: On his own computer, Sean looks up his son's file, which states the boy died immediately and his date of death was September 9th, 1991. When Eve and Castor (as Sean Archer) are at the cemetery, the date of death on the headstone is September 24th, 1991. (00:21:15 - 01:14:50)
Continuity mistake: When Castor (as Sean Archer) is speared, as he stands there singing morosely his shirt is drenched in blood, but when he is next seen in the ambulance that blood on his shirt has vanished. Additionally, the cuts on his face produce blood trails which smear, when he is first speared, but in the ambulance his face is cleaned up and the blood trails are thin and neat.
Continuity mistake: When Archer and Dubov are making their escape, Dubov falls over the rail and Archer catches his gun barrel then tries to save him. In the last shot before Dubov falls, Archer is holding on to the very last tip of the gun, but in the wide shot he is holding a lot more of the barrel.
Revealing mistake: In the big speedboat scene near the end, when Cage is hanging off the side of the boat the stunt double is obvious in wide shots, where the entire boat is visible from above. He has big long sideburns, which are in stark contrast to Cage's short hair, visible in closer shots. At various other points in the movie, stunt doubles appear of much different physical builds than the two actors, with markedly different hair colours, and I seem to recall that at least one of them had facial hair.
Revealing mistake: At the boat scene when Archer is holding on to the red boat and is skiing on the side, you can clearly see the waterproof boots he is wearing.
Visible crew/equipment: On the runway, two shots after Castor Troy says, "This is a big gun. Fly the f*ing plane," there is a side shot of the Hummer. As the camera pans in closer, the reflection of a crew member on the filming vehicle, which moves beside the Hummer, becomes visible at the Hummer's back end, just before it cuts away. (00:10:25)