Factual error: In the beginning, when the President and First Lady disembark Marine One and walk toward the White House, you see the White House. The problem is that it's a set and only the center of it appears. The East and West portion of the main mansion are just sunny blue skies. (00:01:50)
Continuity mistake: At the beginning, when the president lands in the helicopter, the shots go back and forth between the rotors spinning, and the rotors stopped. (00:02:10)
Continuity mistake: When President Mitchell arrives at the White House by helicopter someone hands him the leashes of his two dogs. Mitchell winds the leashes around each other almost all the way down. In the next shot the leashes a completely separate again. (00:02:15)
Continuity mistake: When President Mitchell has a staff meeting after he arrives at the White House by helicopter, there is first one, then two empty chairs between him and Alan Reed. (00:04:50)
Continuity mistake: Duane and his Secret Service colleague wait for Dave at his home to ask him to double for the President. When Dave sees them as he comes out of the kitchen he has a bottle in his left hand. When the camera angle changes the bottle is gone but reappears in the next shot. (00:08:00)
Continuity mistake: At the end of Dave's first entrance as President Mitchell in the hotel lobby, Duane grabs him by the arm and pulls him away from the crowd. When the camera angle changes Dave is surrounded by other security staff but Duane isn't there. (00:14:20)
Continuity mistake: When Dave is taken to the Oval Office for the first time the items on the President's desk shift around from shot to shot, especially noticeably a little glass paperweight. (00:19:20)
Continuity mistake: When Dave is examined on his bed by a doctor he is rested first against two, later against only one large pillow. (00:26:45)
Continuity mistake: When Dave starts working as President Mitchell after his 'illness' and sits down behind the desk the chair topples over backwards. It's a funny scene but, according to even the lowest office furniture safety standards, absolutely unimaginable. (00:28:30)
Continuity mistake: When Dave starts acting as President, Bob asks him to call his company to tell them that he is going on a trip. When he makes the call and the camera angle changes the glasses he was wearing are lying on the desk. (00:28:30)
Continuity mistake: Dave makes a submarine sandwich for Duane and himself. He is seen shredding some carrot on the still open sandwich, then talking to Duane without moving his arms, and finally there is a close-up where he cuts the closed sandwich into half. (00:40:35)
Continuity mistake: When Dave and the First Lady go to the homeless children's shelter in the President's limo her skirt slips off her knee. Her hands are folded on her left side, as she was trying to lean away from Dave, but when we see the knee from Dave's perspective her hands are folded in the lap. (00:42:50)
Continuity mistake: When Dave is under the shower and the First Lady talks to him the handles change positions many times during the scene. (00:47:55)
Continuity mistake: When Dave is thanking his friend the accountant for his help, he puts his hand on the car and when the camera angle changes to a wide shot, his hand is no longer on the car. (00:59:10)
Continuity mistake: When the First Lady joins Dave while he is playing with the horse race game they sit down on the far ends of the sofa with at least a meter between them. When we see them from behind they are sitting right next to each other. (01:00:25)
Continuity mistake: When Dave and the President's wife are going down the elevator to see the real President, right before the elevator stops she unfolds her arms and her hands are at her side. The elevator door opens and her arms are folded again. (01:01:50)
Factual error: When the real president is shown in a coma in the White House basement, he is on a ventilator (a breathing machine). Ventilators require that the patient be intubated (a tube placed into their windpipe) and cannot work with an oxygen facemask which the president has. (01:02:40)
Other mistake: When the real First Lady and the fake President emerge from the secret passageway leading to the fountain, there is an extremely bad process shot of the White House, which jumps visibly. (01:06:10)
Continuity mistake: When Dave and the First Lady escape from the White House, you can see that she is holding a bag of groceries before they get to the grocery store. (01:07:00)
Continuity mistake: On their escape from the White House Dave and the First Lady get stopped by the police. When Dave starts to act as a Mitchell impersonator he puts on his glasses. There's some fluff hanging from the ear piece which is gone in the next shot. (01:08:35)
Chosen answer: Dave and the First Lady snuck out of the White House via a secret underground route which Dave, inexplicably, knew about but the First Lady didn't. The passage led them from inside the White House to an outside location, nearby where Duane of Dave's secret service detail had left a car for them to use. It's still implausible that they could circumvent the remaining Secret Service in making their sojourn, but that is the disbelief that we, the audience, are asked to suspend for the sake of advancing the plot. Upon returning, the couple drive up to the entry gate, where the guard, seeing whom he believes to be the President and First Lady, lets them return to the house. Their only explanation?"The President wanted some ice cream." The MORE implausible question would be how the guard simply trusts that two look-alikes driving up to the White House unattended in a non-government car with a lame excuse would simply let the two pass without consulting the secret service, who should have informed him of the President's comings and goings?
Michael Albert