Factual error: When Stallone shoots the tanker to show that it's being used to transport cocaine, he's apparently stumbled onto the only drug dealers who don't ship cocaine in bricks. There is no way that the coke would flow out of the bullethole like that.
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 you see Conan on the surveillance screen inside the prison, screaming, "Bring them to me!" his hands are at pretty much shoulder level on the bars. But, in the very next shot of him, his hands are much lower on the bars, not even in the shot.
Other mistake: After Tango and Cash go down the chute and into the boiler room, Conan approaches them and says, "On the road, this pig and his cop friends broke my ribs, my leg, and my jaw" without an accent. All of the other lines that he had before, he had a Mexican accent. It also seems like all of his other lines after that point are said without an accent as well.
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. (00:08:00)