In the scene where Jack Lemmon is at the State Department early in the movie trying to get information about Charlie, there is the presidential portrait of Richard Nixon on the wall in the background and a more personal photo of him on Marine One on the credenza behind the desk. That photograph, with fingers in the V-peace sign, was taken upon his final departure from the White House in 1974 and could not have been on someone's desk in 1973.
In the opening scene, as Charlie and Terry are getting out of Capt. Tower's car, Terry opens her door just a bit and pauses, as Capt. Tower hands her his card. Shot is from outside the car on Terry's side. In the next shot, from Capt. Tower's side, the door hasn't been opened yet.
The opening credits roll on a shot of Charlie looking out on the street from the back seat of Capt. Tower's car. The window covers about half of his face, so it's a little more than halfway down. In the next shot showing the car, Charlie is still staring out the window (hasn't moved), but the window is most of the way down.
When the consular guide picks up Ed and Beth at the Christian Science Reading Room for their tour of the hospitals, it is pouring rain. They use umbrellas before getting into the car, but as they drive off the driver's window is rolled halfway down and he isn't getting wet.