Romberg was Hungarian, not Viennese.
The song sheets shown at the beginning the movie have bold, high-contrast drawings on a glaring white background and give only the title of the song. Song sheets of the period would have had elaborate drawings or photographs on a soft white or pastel background and would have included the names of the composer and lyricist and of the singer who introduced the song.
The dinner given for Romberg before the premiere of Artists and Models is very uncoordinated. At his table, there are service plates on the table and entire loaves of sliced bread, so the diners have not yet begun eating. At the table behind, a waiter is pouring coffee.
When Ann Miller is singing "It", she takes off her beads and drops them over the head of a male dancer dressed in a yellow sou'wester coat. Immediately after, she gives a little scream, and the beads have vanished.
Songs are not presented in the correct chronological order in which they were written, nor from the shows in which they were introduced. For example, "Maytime" was a 1917 show, not a 1920s show, as presented here. "Softly, as In a Morning Sunrise" came from "New Moon" (1928) and was not written a decade earlier for Gaby Deslys; "It" was from "The Desert Song" (1926), a much later show than "Artists and Models", as presented here.
When the movie opens, characters wear clothes of the World War I era in which it is set. They continue to wear the correct clothes for the period until the mid-Twenties, when they wear clothes in the style of 1954, with only a few touches to suggest the period.
No mention is made of Romberg's first marriage.
'Frau Mueller' (portrayed by Helen Traubel) is a fictional character created by MGM writers, and bears no resemblance to any real person with whom Romberg was ever involved; Romberg's Manager, Townsend, portrayed by Paul Stewart, and two associates, Judson and Butterfield, portrayed by Jim Backus and Douglas Fowley are also fictional, as also is the show they are supposedly writing, referred to as "Jazzadoo".