Continuity mistake: When Nathan and Bishop are on the rooftop talking, Bishop is seen pulling a chair over so he can sit down. The camera angle changes and he's seen pulling the chair over again.
Continuity mistake: When Nathan starts making his lunch plate from the food that is in the room, he is seen grabbing a spoon but after the camera angle changes to a front view the spoon is not in his hand nor on his plate.
Continuity mistake: Right after Bishop makes it to the balcony, the scene changes to them in a bar drinking and you see Nathan taking a drink and then putting his glass on the bar. The camera angle changes to a close up and the glass is now near his mouth.
Continuity mistake: During Bishop's first mission for Nathan, he kills a general in Vietnam. The first shot hits the general in his chest on his right side. The second shot hits the general in the head, but the bullet hole from the first shot is now gone.
Continuity mistake: As Bishop is pulling the doctor through the mob of people you can see someone has the back of Bishop's shirt and is trying to hold on to him. The camera angle changes to a front view and no-one is holding onto the back of his shirt anymore.
Continuity mistake: When Nathan is training Tom, they are in a park and Nathan tells him to extract info from someone. Tom unfolds his arms and starts walking towards a woman. The camera angle changes and he is seen unfolding his arms again.
Continuity mistake: When Bishop gets the the medication past the checkpoint for Elizabeth, she is seen greeting a man with a handshake and when Bishop goes to take a picture of them, she is seen greeting him again with the handshake through the camera lens.
Continuity mistake: When Nathan stands and greets Agent Folger for the first time he is seen sitting back down on the TV monitor but as the camera angle changes to back inside the room, he is seen sitting down again.
Continuity mistake: In the part where Brad Pitt arrives at the camp to get the doctor, there's a man with a mutilated arm there, but right after that in the bombing scene the same man is there being retrieved from the building.
Continuity mistake: When Nathan shows the doctor the picture of his parents murder scene, the doctor puts his hand over his mouth. The camera angle changes and the doctor's hand is no longer on his mouth.
Continuity mistake: In the scene where Muir shows Bishop the pictures that prove Hadley´s connections with the Hezbollah, he reaches into his pocket and he takes out one picture only. Yet when Bischop looks at it on the table there are three nicely aligned pictures.
Continuity mistake: When Nathan and Tom are on the rooftop talking, Nathan gets up to leave and Tom is facing to his left. Camera angle changes to a wide view and he's looking at Nathan but when the camera angle changes to a closer view he is once again looking to his left. Happens about 3 times during the entire scene.
Continuity mistake: When Bishop goes to get the doctor he pulls up to the campsite and the items hanging from his rear view mirror are swinging all over the place. The camera angle changes to a driver side view of Bishop getting out of the car and nothing is moving anymore.
Continuity mistake: In the scene where Redford asks his secretary to hide Pitt's file, justifying his paranoia with a Noah reference, he puts on his jacket and walks toward the door, leaving the collar slightly upturned. The camera goes to her and then back to him, but when it returns, his collar is perfect.
Continuity mistake: As the van filled with explosives is driving towards the hotel, you see a guard grabbing the doctor and pulling him away. The camera angle changes to a wide view and you see the guard pulling the doctor away again.
Continuity mistake: Towards the end Commander Wiley is given the order to start operation Dinner Out. The on screen titles indicate that he is near Su Cho but at every other point in the movie it is spelt as Su Chou.
Continuity mistake: When Nathan is making a plate of food, he takes a napkin and puts it under the plate. The camera angle changes to a close-up and the napkin is gone. The camera angle changes to a wide angle and the napkin appears again.
Answer: Muir has become frustrated with the CIA as a whole - now carrying out bugging ops on trade talks so the US can sell more "toaster ovens", as opposed to the 'righteous' work he's done all his career. This is compounded when he sees that the CIA are prepared to let a man (Bishop) be killed over it, which also cements his determination to stop it. Although he has underestimated Bishop's feelings and determination to rescue Hadley, that's not really the point. He sees that Bishop is doing something righteous, 'the right thing' so to speak, and sees rescuing Bishop and Hadley as a chance to a) do something worthwhile again before he retires, b) redeem himself for past sins (sacrificing people/Hadley), and c) poetically stick it to the CIA - using their own resources to carry out the rescue mission amidst the trivial 'work' they're doing now. Muir knows that when he retires he'll be broke, but he'll be able to live with himself - he did something that was morally the 'right thing', as opposed to being the cold calculating operator he's been all his career, with that conditioning being another reason he now resents the CIA (he doesn't like what he's become). He's kicked against the bureaucrats who are doing all the wrong work for the wrong reasons. Also, there's a parallel between Bishop's feelings for Hadley and his attempted rescue mission, and Muir's feelings for Bishop (he loves him like a son or a star student). Muir certainly sees Bishop as family, and you don't mess with an Amercan's family. Muir says as much in the film with the analogy about his uncle's plough horse. The student is now teaching the master - about doing things for the right reasons (love and loyalty as opposed to death and toasters).