Factual error: When they show the Nelson Eddy song 'I Love You', the set/movie shown is Rose-Marie. But that number is from Rosalie not Rose-Marie. Two totally different movies - one set in West Point not with the Canadian Mounties. There are no Cole Porter songs in Rose-Marie, likewise there are no Mounties in Rosalie. Rose-Marie's music was by Harbach / Hammerstein II / Friml / Stothart. (01:09:25)
Factual error: When Cole Porter sits in on the "Kiss Me, Kate" rehearsal (when the cast is singing "Another Openin', Another Show"), he calls the soloist by name - Ms. Morison. This refers to the original leading lady, Patricia Morison. However, the main vocals for "Another Openin', Another Show" are sung by a completely different character than the one originated by Patricia Morison. In fact, Morison's character does not sing at all in that musical number.
Revealing mistake: In an early scene Cole and his future wife watch fireworks over Paris through a doorway overlooking a balcony. The explosions are reflected on the glass of the open door, which is at an angle to the POV. But the CGI fireworks and their reflection in the glass are squashed to fit into the foreshortened pane of glass. In reality the reflected image would be like any mirror, with the image inverted left-for-right.
Deliberate mistake: Throughout the film, scenes of several Cole Porter productions are shown being performed. These scenes all contain a well-known musical number. Two scenes in particular (after the Alanis Morissette number and immediately after the "So in Love" duet) end with the lead singer/singers bowing to the audience and then waving the other cast members on stage to take a company bow. The problem is that neither of those numbers appear at the end of the shows being "performed." The "So in Love" duet, for example, most definitely appears in the musical "Kiss Me, Kate" well before the Act Two finale. I assume that these mistakes were filmed deliberately to emphasize the importance of the songs in question, but they are still errors.