Factual error: The opening shot (of the New York Stock Exchange's trading floor) has the subtitle "1985," which might lead one to expect that at least the action in the first few scenes takes place in the year 1985. However, when Charlie Sheen is talking to his Nimrod broker buddy the Nimrod jokes that the day the Challenger exploded, Gekko was on the phone "selling NASA stock short." The Challenger exploded in January, 1986, not 1985. [An explanation for this: Wall Street, as conceived and filmed, was supposed to be set in 1987. However, near the end of 1986, The Ivan Boaesky insider-trading scandal hit, many rules were changed, and acknowledging those events would have undone much of the plotting of the movie. So the movie was shifted back in time to 1985 (before the scandals, and also before the Challenger disaster), thus creating this major goof].
Plot hole: The scene in Central Park where Bud tapes Gekko never would have happened. Gekko's comments imply that he was unaware of Bud's arrest earlier that morning (not just that Gekko was unaware he was being taped). (1) Gekko makes comments that the Feds are pleased with, at least to some extent incriminating himself. (2) Gekko doesn't say something like: "OK, now you've been pinched, here's what you do." BUT - how in the world would Gekko not know of Bud's arrest? Even in the days before the internet, information spread like wildfire on Wall Street. All the brokers in Bud's office would be on the phones saying "they just arrested Gekko's broker!" Everyone on Wall Street, especially someone like Gekko, would find out, and far more quickly than the time it took to schlep Bud up to Central Park and strap a recorder on him.
Continuity mistake: After Bud asks Carl for money at the bar, a friend comes up and Carl shakes his hand. At this time Carl doesn't have glasses on. Bud then asks Carl "How's work been treatin' you." When he asks this the camera angle is over Carl's shoulder and he has glasses on. Then in a front shot, the glasses are in his hand, but there was not enough time for him to take them off.
Factual error: After Bud's conversation with Gordon in the park he goes to a restaurant bathroom. The agents are waiting for him. He open his shirt, they rip the tape recorder off of him then immediately begin to play the conversation. It picks up right where the evidence is. No one had time to rewind the tape.
Continuity mistake: When Gordon and Bud are getting dressed after playing racquetball, Bud is seated with what looks like a can of soda on the bench to his right. He drinks from the can. Less than a minute later when Gordon says, "I've been in this business since '69," Bud drinks from a glass.
Continuity mistake: When Buddy first meets Gordon Gekko, Buddy is depressed as he walks towards the door of Gekko's office. The door is opened, and as Buddy turns to look at Gekko his tie is perfectly placed. In the next camera angle of Buddy walking out of the office his tie is pulled down.
Continuity mistake: When Bud and his father are in the Owl Tavern discussing the FAA ruling for Bluestar, Carl says, "We can go for those new routes to Pittsburgh and Boston now. We're gonna compete with the big guys." With his right hand, Carl drinks some of his beer while his cigarette is left in the ashtray. When the camera angle changes to Bud, his right hand is holding the cigarette.
Visible crew/equipment: A cameraman with a light coloured, short-sleeved shirt is visible (operating a large camera) when Gordon says "Interesting, got a card?" in Bud's first encounter scene. You can see him on the back wall when you look past Gekko - the wall where the door is located but closer to the main window.
Continuity mistake: At Gekko's party Bud is introduced first to Sam Ruspoli, Carmen Winters, then Stone Livingston. After Bud shakes hands with Ruspoli he extends his hand to Winters who remains seated. When the camera angle changes Bud shakes with Livingston but the handshake with Winters has been cut from the footage. The changing camera angle reveals another error. The paperwork that Bud gives Gekko inside his front door is now folded in half but the action to fold the papers has also been cut.