Continuity mistake: When at the "indoor shooting range", Davies is shooting the gun with his right hand, but lowered it with his left.
Revealing mistake: At the start, just as Moreau rides up the stone road leading to the monastery up ahead, before he passes the two guards we can see that it's a flipped shot - note the backwards license plate number.
Factual error: George Smiley stays in a hotel near Liverpool St Station, London to investigate the spy at the heart of the circus. There is one scene where we see, from above, a train leaving the station. Liverpool St station is electrified using overhead wires - the train is leaving a station using a different electrification system called 3rd rail which has never existed at Liverpool St.
Continuity mistake: In the scene on the Golden Gate Bridge when the apes are pushing the bus, the police shoot the bus numerous times, but when the camera goes off the bus and then shows the bus again (twice) the bullet holes are not there anymore.
Continuity mistake: At the campground, when Hanna and Sophie are under the blankets together, each girl is shown throughout the conversation laying on her left side. If this were actually the case, they would both be facing the same direction, not facing each other. (01:00:45 - 01:03:30)
Plot hole: Everybody jumps into the water and emerges on the submarine except for Natalie. They're wondering where she is when they notice a flare. They realise it's her, and they send a search party. She's hiding on a bus maybe one to two kilometres away from the water. Her going there makes no plausible sense. Makes no sense how she held her breath underwater longer than anybody that they didn't see her and why she would go in the opposite direction of the sub. It was done to prolong the scene. (01:09:00 - 01:18:00)
Factual error: Upon hearing that the bombs will drop in 3 hours time on Santa Monica, one marine sets the countdown timer on his watch for 3 hours and starts it. The watch is a Casio G-shock GW-9000 Mudman. This particular watch only has a 1-hour countdown timer. (00:24:15)
Character mistake: When the EMTs are resuscitating Dr. Harris, they use a defibrillator despite their being on a wet metal dock. Not only is this highly dangerous to absolutely everyone present, it would be completely ineffective at restarting his heart as the water and the metal would dissipate the electric current too much for it to do any good. At the very least, they would have stabilized his spine then moved him to a dry surface before beginning defibrillation. (00:08:30 - 00:09:10)
Suggested correction: External defibrillators are self grounded and so can be safely used on wet or metal surfaces. https://danboater.org/travel-health-and-safety/are-aeds-safe-to-use-in-wet-environments.html.
AEDs are indeed safe to use in wet areas - but in the film, it is not an AED that is used. AEDs are automated, and not operated by humans, so as to reduce risk. Your link explicitly states the rescuer must not have direct contact with the body: they just apply the pads, then move back. In the film, it is shown in detail that the medic applies the paddles and then operates them while still in contact with the body. The mistake stands: it's a traditional defibrillator, thus incorrectly used.
Continuity mistake: During the bridge collapse scene, when Olivia is crawling on the beam, she is first seen on the part of the beam that is closer to Sam. Almost instantly afterwards, she is on the part of the them that is closer to Molly. The space between the two beams increases significantly between the two shots as well.
Continuity mistake: During the film, Daniel Craig's character rides out to the house where he last saw the woman he was in love with. During the wide shot showing him on his horse riding toward the camera, the device on his wrist is missing. It is obvious if you are paying attention, as he is using the arm which is supposed to have the device to hold the reins of the horse.
Factual error: The Song "Looking for the Magic" by the Dwight Twilley Band plays on repeat several times throughout the movie, however it comes up as track 1 on the CD player each time."Looking for the Magic" was never the first track on a Dwight Twilley CD - It was track 2 on the group's 'Twilley Don't Mind' album released in 1977. You can tell the disc is not a homemade mix CD by the printing on the top of the CD the first time it is placed in the tray.
Visible crew/equipment: When Jack arrives with the shopping, a crew member in shorts is reflected on the glass. Clearly not Max.
Factual error: In the scenes of Ian Fleming in the Naval Intelligence HQ, there is a map of Scandinavia on the wall. The map already has the post-war borders of Finland on it.
Character mistake: Nicole Johnson, a criminology professor, after enumerating a number of facets of jurisprudence, states that following these tenets is, "The only way the criminal justice system can ever be perfect." As a professor, she is surely aware that, despite following the pronouncements in the referenced book, criminal justice is far from perfect.
Continuity mistake: When Boyle arrives in his police car at the house where McCormick is murdered, he turns off his engine and his windscreen wipers are pointing towards the sky. In the next shot you see the windscreen wipers in their normal position again.
Continuity mistake: In the restaurant scene Nathan has a glass in his right hand on the table. The next shot appears the glass on the table without his hand, and then again in Nathan's hand.
Factual error: Near the end of the movie, when they go to steal the boat, there is a Puerto Rican flag in the front of the boat. This flag has the royal blue triangle, instead of the light blue that would have been in the 1960's such as all the other big flags used on poles.
Factual error: In the climax of the movie, Nicholas Cage uses a nail gun like a marksman, hitting with precision the bad guy that holds his wife tight. Besides this skill of his coming out of left field, a nail gun does needs a surface against the opening. It does not shoot nails in the air without pressure being applied, it's a Hollywood trope. (01:18:45)
Continuity mistake: Charge gets to the laundry mat first, and sees a TV on. He sets his map down in front of it, and the close up of the map shows the TV is suddenly off. (00:07:25)
Factual error: The movie takes place in Stamford Connecticut (per locations and is shown on cop cars). Eva buys a bottle of wine in a supermarket, but in CT only beer can be purchased in a supermarket. (00:25:15)