When Jim Hardy plays the bells on the Christmas tree at Holiday Inn, he hits the two bells twice, but in both cases, gets different tones the second time. This happens again, almost identically, when Linda Mason plays the bells on the movie set.
The calendars shown for the last part of the film are from 1942, except for November, which is from 1941. The progression of calendars goes December 1941, February 1942, April 1942, July 1942, November 1941, and December 1942. This November calendar portrays the second-to-last vs. fourth Thursday Thanksgiving day confusion, started in 1939 by presidential proclamation, and cleared up by congressional legislation in 1941 for the 1942 calendar.
When Jim enters Ted's Hollywood dressing room, he has his pipe on the left side of this mouth. The next shot shows it on the right side, although he has had neither time enough, or his hands free to move it.
In one of the final scenes, the Hollywood set of the inn, Jim Hardy sets his pipe down on the piano. A few minutes later, when Linda Mason reaches for it to tap the bells of the Christmas tree, it has changed position.