In the opening scene on the fishing boat, Lee Evans is shot at and dives into the water. The long shot shows the boat is stationary in the water, when it should be moving, according to the plot.
In the same scene a man has both his feet amputated by the propeller of the other boat. He is seen wearing socks and shoes, but moments later, the foot floats past without shoe or sock.
When Tommy Fawkes gets the Parker brothers to sign the contract for their act, there is a continuity issue with the chair. The Parkers stand up and go to set up the scene to show Tommy Fawkes. From a high shot you see Tommy Fawkes stand up and turn his chair around. It then cuts to the front of Tommy. His chair is in its original position and he turns it around again to the position he did in the first high shot.
During the final scene, while the camera is showing the police at the base of the pole, a spotlight is throwing a very clear shadow of the camera, complete with 'rubber ducky' antenna on the actors.