Revealing mistake: As Kevin is flying off the front porch on the toboggan, you can see the small wheels mounted on the bottom of the sled to aid in its "jump". (00:25:30)
Revealing mistake: Riggs handcuffs himself to the depressed businessman. They jump off the building but they're not handcuffed to each other anymore. They used plastic cuffs which could separate during the stunt in case anything went wrong. They break just as they jump, so they grab each other's hands to stay in contact. After they land the cuffs are attached again. (00:31:00)
Revealing mistake: When Hans discovers the first bad guy lying dead in the lift ("Now I have a gun - HO HO HO!") and pushes his head, the corpse is moving his head before he is hit (watch carefully). He also closes his eyes before Hans makes contact. (00:39:15)
Revealing mistake: In one scene, the Penguin is making a "bat" shadow puppet on the ceiling. But there's no light behind his hands. If there's no light, there's no shadow. (01:03:45)
Revealing mistake: In the skywalk scene, when McClane pushes the paint stand on the terrorist, it is quite obvious that they use a dummy when the paint stand falls on the terrorist and crushes him. (00:45:05)
Revealing mistake: When the professor is trying to find the gremlin, he is in the room with the movie playing. The projector that is playing the movie is actually moving backwards. (00:44:35 - 00:47:35)
Revealing mistake: In the scene on Christmas morning when the Bumpus' dogs run in and eat the turkey, during the shot of the dad sitting in the chair reading the comics, one of the dogs bumps the camera and jostles it a little bit.
Revealing mistake: During the ghost of Christmas present, Kermit is walking with tiny Tim on his shoulder and you can tell Kermit is walking on a spinning drum. Right before the camera pans away you can see Kermit's feet slide like he stopped walking but the road kept spinning. (00:55:00)
Revealing mistake: In the beginning of the movie when Charlie is in the gym, the last can of spray paint he uses, just before the Principal catches him, appears to spray 'clear'.
Revealing mistake: Take a good look at the lower right corner during the 'Hearts on Fire' training sequence at a barn in Russia. Rocky does a few leaning sit-ups; at that moment the cow in the lower right corner moves backwards. When you look closely you'll see it moves back too quickly and anatomically incorrectly, thus revealing it's a fake head attached to wheels or something. (00:57:45)
Revealing mistake: Towards the end when Harmony calls Perry's phone as she's lying on the ground, Harry grabs the phone and looks at the caller ID to see her name. Unfortunately that's not the display showing who's calling. Anyone who has a Nokia phone will recognise that that's showing the contact list with just two entries - Harmony and a random number. The fact that it says "contacts" at the top of the screen is a bit of a giveaway.