Revealing mistake: In Frank and Sarah's first conversation her headset is on mute, shown by the fact it's blinking red.
Continuity mistake: At the airport, Sarah says "She has a camera in her purse, we have to kill her?" As soon as the camera stops panning around, Marvin is visible in the far background holding the pig teddy with the pig's legs facing the two. The shot then cuts to a close-up of Marvin. In this close-up, the pig teddy's legs are now facing the opposite direction.
Factual error: In the very first shot of the movie, a clock is shown ticking. The time on the clock reads 05:59:56. It is obviously AM because a few seconds later at 06:00:00, Frank wakes up as if it was morning. As Frank sits up, clear daylight is visible outside of the window. This scene is supposed to be set during winter. We know this because there are many Christmas decorations. Since this is meant to be winter, it should still be dark at that time of day.
Continuity mistake: The Vice President begins a speech at the Victory Fund Gala. Cooper, backstage, then exits the room. Before he walks over to the door after exiting the room, he has an ear piece in his right ear. The ear piece disappears when he walks through the door in the next shot.
Continuity mistake: After Frank injects the assassin, the syringe injected into his neck is horizontal. However, when one of the assassins shoots a grenade inside, the same assassin that Frank injected now has the syringe in a vertical position. Frank never moved the syringe, nor could anyone else since they were dead.
Continuity mistake: In the scene after Sarah mentions the book "Love's Savage Secret", Frank is then seen lying in bed reading the novel. Notice how he uses reading glasses in this scene. In the shot where the camera is in front of Frank after the shot of the page, we can see nothing is reflected in his reading glasses. In the next shot, the page (or lamp or similar), is suddenly reflected in his reading glasses. This can't have anything to do with the angle of the camera because both shots are in front of Frank, just in different close-ups.
Other mistake: In the end credits, the cast is meant to be in order of appearance. When it gets to Victoria's credit, it states that Alexander Dunning appears next in the movie. Another 4 people after this reads Cooper's family appears. This is wrong. Victoria appears. A few minutes after this, Cooper is shown at his house and watches his kids sleeping. In the scene after Alexander Dunning appears for the first time in the movie. For the credits to be in order of appearance correctly, it would have to be Victoria - Cooper's Daughter - Cooper's Son - Alexander Dunning.
Continuity mistake: During the airport shootout, Frank tells Marvin to unzip his pig teddy that is revealed to contain a grenade launcher, and he shoots at a gunner on top of a container. Marvin then drops the pig teddy, which is visible in front of the containers as they take off running in the next shot to the next container. However, when the shot zooms out as Marvin points his middle finger at the satellite, the pig teddy is no longer there. It couldn't have been out of frame because the pig teddy was only two containers away from them.
Continuity mistake: Frank and Sarah arrive at a motel and Frank removes the duct tape from Sarah's mouth. Sarah then says "If you let me go now, I won't press charges". Note the two necklaces around her neck when she says this. There is a butterfly attached to one, lying above the other necklace. The shot then cuts over to Frank. When the shot returns to Sarah, the butterfly is now several inches below the other necklace. Once again, the shot cuts to Frank where he then says "I was in the CIA". In the shot after that shows Sarah again, the butterfly has gone back to lying on top of the other necklace. She could not have moved the necklace around during the shots of Frank since she was tied up.
Continuity mistake: After killing all of the assassins, Frank places bullets in a frying pan and turns the stove on. When the bullets go off, the rest of the assassins start shooting at the house, destroying a snowman on Frank's porch. In all future shots of the porch afterwards, not only has the snowman disappeared, but there's also no sign of the snowman's remains either.
Continuity mistake: Near the start when the assassins come after Frank, Frank injects one with the syringe that was intended for him. The half of the syringe that has no liquid has a noticeable plastic grey color. It then cuts to the close-up, and the half with no liquid now has no grey color.
Revealing mistake: Alexander Dunning tells Agent Cooper to handcuff Frank. After Cooper handcuffs Frank it then cuts to a close-up of Frank's hand, showing Cooper giving him the key to the handcuffs. In this shot, we can see that the cuffs aren't actually locked in. He obviously is supposed to have locked the cuffs since he gave Frank a key to unlock them - if he faked it, why the key? This is most noticeable when Frank clenches and lowers his hand after being given the key, giving away the loose cuff.
Continuity mistake: In the Russian Embassy, Frank meets up with Ivan. During this scene, Ivan opens a bottle of vodka. In the shot after Ivan says "As we get older, things seem less important", it is visible that the bottle is filled to the top. He then takes out two shot glasses and fills the two of them up with vodka for both him and Frank. When Igor says "To Igor. The Butcher", we can see that the level of vodka has gone down by a far smaller amount than two shots' worth.
Continuity mistake: When Frank meets Sarah in the flesh for the first time, she throws numerous items at him. When she picks up a candle holder and throws the candles at him, a third of one of the candles remains stuck to the holder. After Frank tells Sarah, that people are trying to kill them, Sarah replies "Why would anyone want to kill me?" In this shot, the third of the candle is currently on the right hand side of the candle holder. Then when Sarah says "Why?" after Frank says they've been listening to their conversations, the third of the candle is now on the left side of the candle holder.
Continuity mistake: Just after Frank knocks out Alexander Dunning, the scene cuts to Sarah and Victoria having a conversation about how she met Frank. At one point during this conversation, Sarah says "Of course now I'm a fugitive and the CIA wants to kill me and I'm hiding in a hole". Right at the end of the shot where Sarah says this line, it can be noticed that her lips are apart. In the immediate following shot her lips are fully closed.
Character mistake: In the scene where Bruce Willis, Mary-Louise Parker, and John Malkovich are having lunch outside on a river in New Orleans, right after Mary-Louise Parker gets off the pay-phone, John Malkovich reads off the tail number of a helicopter flying over as "N9745C", even though the number is visible as "N9748C". A few minutes later, when the three are talking to James Rema in Mobile, in the airport control tower, they see the helicopter (again, visible as "N9748C"), only this time, John Malkovich correctly identifies it as "N9748C".