Deliberate mistake: In the sequence where Jack finds his friend, and then the cards he is holding counts down to the explosion. Jack runs out, and the house explodes throwing the cop car into the air. If you look close, you can see the piston that launches the cop car and then falls back down. (00:24:40)
Suggested correction: This is a scene in the "fake movie" where everything is an action movie cliche, including seeing the deliberate mistakes.
Deliberate mistake: Just before Danny enters the action movie, Jack Slater (Arnold) arrives at his 2nd cousin's house. Jack exits his car and jams his desert eagle pistol into his waistband. He then approaches the front door where he turns toward the camera to kick in the door. You can clearly see there is no gun in his waistband now. In the next shot he draws the gun from his waist. (00:22:50)