Factual error: At the end of the scene where CC Baxter meets the doctor for the first time in the hall, Baxter is standing in the doorway of his apartment as the doctor enters his own apartment. From that view, you can see into Baxter's kitchen, which has a window - right where the apartment the doctor just entered is located. That could not be an outside wall.
Factual error: People show up to work on 24 December (Christmas Eve), on the 26th, and on the 27th, but this would make sense only if the 24th was a Monday or a Tuesday. However in 1959 (as narrated by Jack Lemmon at the start of the movie) Christmas Eve fell on a Thursday, making the 26th/27th the weekend. Also, early in the movie C.C. Baxter says to a colleague at the office that "Mr. Heidelberg had a Halloween party last night", implying that it is November 1st, but in 1959, November 1st fell on a Sunday and Baxter would not have been at the office.
Factual error: Jack Lemmon at the beginning of the movie lights up the pilot flame of his stove, puts a frozen dinner tray straight from the cardboard box in the refrigerator, and it's all nice and ready for him to eat (the aluminum foil is so hot it burns his fingertips, even!) in the minute and a half it took him to put the bottles out of the door and talk to his creepy doc neighbour (no cuts are shown to imply passage of time). (00:08:00 - 00:09:30)