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)
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)
Factual error: At the beginning when Dave is imitating the president in the car dealership commercial, he's talking about the specials on the Geo Storm and Geo Storm convertibles. Geo never made a Storm convertible. The only convertible car sold under the Geo nameplate was a convertible version of the Geo Metro, based on the Suzuki Swift.
Factual error: Near the start of the movie Kevin Kline as the real president gets off the helicopter while the rotor is still spinning. The president never gets off Marine One until the rotor has stopped.
Factual error: Nance give the President fertility beads from the King of Togo. Togo is not a Kingdom - it's a Republic.
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