During the rehearsal of the song "I Get A Kick Out Of You" at Cole Porter's mansion, a butler uncorks a bottle of champagne. The force of the uncorking knocks the towel off his arm. A second later in the next shot, the towel is back on his arm.
When Cole talks to his mother at Christmas, he places his gifts on a table and a long, thin box is leaning against other packages. When the scene cuts to show the packages again, they are neatly stacked.
As in Kiss Me Kate, Cole Porter is depicted as a healthy man who is capable of walking for most of the film. In fact, he was a cripple needing constant medical care for his shattered legs which were the result of a riding accident in 1937; any scene showing him walking after that date is in error.
In the movie, it is implied that the U.S.S. Lusitania was sunk the same night as Porter's Broadway play "See America First" debuted. In fact, the Lusitania was sunk over 10 months before (May 7, 1915) the play opened (March 28, 1916).