Continuity mistake: When the bearded man is robbing the convenience store, he demands that the owner opens the safe. Look at the Lite cans on the safe. When seen from the right, there are four cans. When the owner kneels down to try and open it, there are now three. When we cut back to a view from the right there are again four. Finally when the robber is shooting at Robocop there are only two.
Continuity mistake: In the drugs factory, when Robocop starts to bang on the door, you can see at least 4 people on the stairs and overhead walkway. After Robocop knocks the door down and looks around, we see this through his view and they have vanished. They reappear when the camera view returns.
Revealing mistake: The film takes place in Detroit, but it is glaringly obvious that it was shot in Dallas. First of all, in the early scene where Murphy chases Boddicker's gang on the highway, Reunion Tower, one of Dallas's most famous landmarks, is visible in the background. Much of Dallas's skyline is also visible in the final scene where Robocop confronts Dick Jones in the OCP boardroom.
Continuity mistake: When the guy holding the mayor hostage gets thrown out of the window, we see the only two TV cameras near the location follow his fall down to the ground. A few seconds later on the news though, the footage is the same shot we saw in the film, staying focused on the window.