Factual error: When it's 00:00 on January 1st, it's not night in Sydney, it's 11 AM. When they 'reveal' stuff at the end of the movie, and they show that things happen exactly at 00:00 in the night in London, it can't possibly be dark in Sydney, Australia.
Suggested correction: It shows that Sydney is at dusk and is becoming dark, so around 5pm-6pm-ish, not 11am during the day.
Plot hole: Prior to the final show, when the horsemen are performing separately at different locations in London. [Scene X] Jack is busy with his card swap trick. While others are doing their tricks too, [Scene Y] McKinney is believed to be tricked once again by his face sharing brother at another location... Dylan gets a call and then he calls everyone to wrap up and meet somewhere. [Scene Z] Jack also wraps up and leaves the place... OK. Later after the expose in final show McKinney tells the story about how Jack successfully hypnotized his brother [in the Scene Y]. How could Jack be at two different locations at the same time? He was performing somewhere else when he did hypnotism at another location and then wraps up his trick back where he started.
Factual error: The movie shows the FBI operating in London in order to capture the Horsemen. The FBI does not have jurisdiction to operate outside the United States, although they can act with agencies in other countries.
Factual error: When Lula is performing her dove tricks in London she's standing by Cutty Sark, a historical ship museum in Greenwich. Greenwich is south of Thames river. When Walter and his company are showing the positions of the Horsemen on the map of London all of them are shown north of the Thames.
Character mistake: Dylan is showing Agent Cowan and the FBI director the pictures of the pigeons and Dylan and Cowan start arguing, while the FBI director continues to look at the evidence on the Four Horsemen. Whilst looking there is an article reading "FBI Investigation Stalls." On the first column of the article, it is mentioned that all four members of the Four Horsemen, J. Daniel Atlas, Henley Reeves, Merritt McKinney and Jack Wilder, all disappeared into thin air at the final magic show, and gave the audience fake dollar bills. By the time of the final magic show, Jack had faked his death and was presumed dead, so only three members of the Horsemen were present, not four. (00:08:55)
Continuity mistake: When Dylan enters Thaddeus' prison cell and begins looking around, there is a clock on the wall showing 7:52. As Thaddeus walks into the cell seconds later, the time on the clock is suddenly 7:55.
Continuity mistake: When Dylan is leaving the prison with Thaddeus, it is night time. But later on in the movie, when the FBI director and Agent Cowan are watching the CCTV footage of Dylan and Thaddeus leaving the prison, the time on the CCTV shows them leaving the prison at 14:10, the middle of the day.
Factual error: After his show Atlas reveals he did his rain trick using rain machines and strobe lights. While this is technically correct it only makes the rain appear to stop, not prevent it from falling. But during his show when the rain is "stopped" we see no splashes on the ground or on people who put down their umbrellas.
Continuity mistake: When Daniel is communicating with "The Eye", he walks over to a well and places his phone down around the rim of it. The phone is beside the edge of one of the blocks covering the rim, to its left. When Walter is explaining to Daniel later on in the movie that he was the voice, the scene cuts to a flashback, and Daniel is now shown placing the phone beside the right hand side of the edge of the block. (00:06:05 - 01:10:55)
Continuity mistake: In the first Now You See Me, Dylan said before his father got into the safe that was dropped into the river he gave Dylan his watch to hold so he could count the seconds until he escaped, but in Now You See Me 2 there's a flashback that showed what happened before his father got into the safe and he does not give him his watch. Instead it shows Dylan and his father both with a watch and synchronizing them together.
Continuity mistake: When the Horsemen are onstage at the OCTA party, Dylan opens his iPad and notices a tarot card on it. In the close-up shot, when the tarot card is first shown, it can be seen slightly passing over the edges of the iPad, but in the shot previously, Dylan is opening the iPad, but the tarot card is nowhere in sight. It would have been visible even from the camera angle that was shown. (00:22:45)
Continuity mistake: When Merritt is explaining to Daniel, Jack and Lula that they are in China, he starts saying "I think where we are right now, they don't refer to it as Chinese food." In this shot, he is standing beside Lula, maybe a few inches ahead of her, but in the next shot, Merritt is suddenly a couple more feet ahead of her. (00:27:20)
Continuity mistake: At the Royal Greenwich Observatory, when Dylan picks up the picture of his father and Thaddeus, he grabs the picture holding the bottom of the left hand side, but in the next shot, he is suddenly holding the picture much further up along the side. (01:55:25)
Continuity mistake: When Dylan and the Horsemen are infiltrating the OCTA party, Daniel is carrying a tray with four different lines of sushi. Daniel then walks into the hallway still holding the tray and the four lines of sushi and their position on the tray have suddenly been reversed. (00:16:55)
Revealing mistake: When Dylan is looking at the news articles in Thaddeus' cell, the camera pans over to one of the articles with the headline, "I am a victim": Thaddeus Bradley. The opening paragraphs on the first column are repeated throughout the entire article.
Continuity mistake: When Owen Case is being introduced at the OCTA launch, Merritt and Lula are backstage and Merritt says "Nice work, lady" whilst putting his hat on. In the next shot, his hands are suddenly by his side. (00:20:30)
Continuity mistake: When Walter Mabry is explaining how the Horsemen ended up in Macau he walks over to sit on the couch to show the slideshow of the plane trip. As he walks over, Atlas is not on the same couch as the other Horsemen, but when Walter goes to sit down he squeezes between all of the Horsemen with Atlas now on the end of the same couch as everyone else.
Continuity mistake: At the magic shop, when Daniel is reading out the list to Li, Daniel first has his right hand on the paper, but in the next shot, he is holding the paper with his left hand. (00:44:20)
Continuity mistake: While Chase and Merritt are drinking in the bar, in one shot Chase is wearing sunglasses, in the next shot the sunglasses have disappeared. (00:48:10)
Continuity mistake: At the launch party, Dylan is holding a playing card with 'The Fool' written on it. Dylan turns the card around whilst holding the card on the right hand side. From a different shot, he is holding the left hand side.