Continuity mistake: When Stallone catches Tango with his sister, he sees a stranger (the Chief) in the screen door in the background. He jumps forward into the door taking it with him, along with the stranger. The shot then shows the door get pretty smashed up, falling apart as they both hit the floor heavily. The next shot sees Stallone picking up a perfectly intact door off a crushed Chief.
Continuity mistake: Towards the end of the movie when they are in their big 4x4 destroying the camp, they jump off a small cliff. It is a night scene so they have their headlights on. They cut outside the truck as it jumps and both headlights work. They go back inside, then outside as it does a hard landing. You can clearly see one light is now out from the impact. They go to another inside shot, then outside after it lands. Both lights now work.
Revealing mistake: When Tango and Cash hold a bad guy upside down off a roof, Tango has his arms straight out in front of him, elbows locked, parallel to the ground. This would require incredible strength. In the next shot he holds the bad guy properly, held close to his own body with his elbows bent - but Tango appears to be exerting no effort in order to lift the guy at the beginning of this new shot. We can also see the outline of a harness system to hold the bad guy up under the black silk shirt of the bad guy.
Revealing mistake: When Cash's stuntman jumps out the window after the bad guy, his feet move out in front of him so that he will land on his back (on an airbag) - cut to next shot and his feet are magically underneath him as he lands and rolls. As (Cash) runs around the street corner it is obviously a stuntman. When Cash runs down the narrow alley he is not wearing a bulletproof vest, but in a following scene he takes one off.
Revealing mistake: When Tango and Cash are getting attacked down the laundry chute, they are tied up above a water tank with a guy holding an electric wire. Their hands are tied to dry cloth which is then tied to the cable. Cloth has no conductivity so there is no complete circuit when their feet are lowered into the water so they wouldn't be getting shocked. The reason they wouldn't be getting shocked is actually explained later in the movie just before they slide down the electric wire.
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Continuity mistake: Tango and Cash play good cop, bad cop with the bad guy on the roof of the building by taping a grenade to his mouth and intimidate him by threatening to pull the pin. They get the information that they need out of him. Cash says "We scared him so bad, he is standing in a puddle and it's not raining". They then take the grenade, pull the pin and stuff it down his trousers. The next shot is the grenade coming out his trouser leg onto the ground where there is no puddle to be found.
Continuity mistake: When Tango & Cash are standing on top of the building, getting ready to run and slide down the wire, the type of t-shirt Cash is wearing keeps changing. It switches between a sleeveless shirt (when shown from the front) and short sleeves shirt (when shown from the back).
Continuity mistake: Cash spins out the truck of the bad guy and it stops all forward momentum, but in the next shot it is racing at full speed. The truck then takes out many overhead fluorescent lights. Why has no other vehicle ever hit those lights? Then the truck partially knocks down 7 lights in a row, leaving them hanging vertically. They were damaged enough to knock them off the ceiling - but they are all undamaged enough to still be operating: keep in mind that these are fragile fluorescent lights. But no damage is done to the floodlights on the roof of the truck.