Revealing mistake: As Mary, Sam, Jarvis and Andrew are speeding away from the TV station, one of the boys from the UFO crashes his bike head first into the car. This causes the boy to crash through the window. When he does this the window shatters like a plate glass window instead of the safety glass that is a standard to be used for vehicle windshields.
Visible crew/equipment: While Mary, Sam, and Andrew are leaving the TV station some guy in a red vest attacks Sam. Sam knocks him down and Andrew hits him with his cane. As the camera pans back up to show Andrew, you can see the film crew reflected in the window of the doorway.
Revealing mistake: When Sam is attacked by the alien hiding on Mary's back (during their first intimate scene) he grabs a red-hot poker from the fireplace. The following close-up of him stabbing the alien, shows the poker to be made of rubber as it bends at the tip each time he stabs it.
Visible crew/equipment: When Sam and the alien controlled Andrew are fighting in the back of the helicopter, in shots from outside the chopper you can see someone sitting in the right hand seat of the helicopter. Only Sam and Andrew went up in the chopper.