Danny Madigan states that after the prefix 555, there are only 9999 possible phone numbers, since only four digits are available. This is incorrect: there are 10000 possible phone numbers. He forgets that the combination 0000 is also available.
When Danny is watching the movie and the ticket activates, Jack shoots the the dynamite which flies out of the screen and lands in the movie theatre, Danny runs towards the screen to take cover. Later, after Benedict leaves the movie, Jack and Danny follow him and land in the same movie theatre and there is no sign of the explosion that would have resulted from the dynamite.
While in the real world (New York) Jack Slater plays a game of chicken with a taxi. When his car starts going down the alley, there clearly is a cable running across the floor attached to Jack Slater's car.
The movie claims there are 9,999 phone numbers that begin with 555-xxxx. In fact there are 10,000 when you include 555-0000. It is better this way since 9999 sounds more mathematical and few people would get it if they said 10,000.
When Jack falls from the broken elevator, the crane is moved right below him so he can grab on to Leo the Fart. However, Leo is not attached to the crane, but when the shot changes, Jack grabs on to Leo the Fart's legs.
Danny's mother has a lengthy conversation with Jack Slater, believing him to be Arnold Schwarzenegger. Yet during their entire conversation, Slater does nothing to make her not believe him to be Schwarzenegger despite the fact that a few simple questions could have certainly stumped him.