Mozart's wife Constanze was pregnant with her daughter Theresia. In the movie she is not portrayed pregnant.
Baroness Martha Elisabeth von Waldstätten is portrayed as a woman in her late 50s. In 1787 the real baroness was slightly over 30, being born in 1744.
Mozart's only daughter Theresia Konstantia Adelheid Friderika is seen before Mozart is leaving to Prague for the premiere of "Don Giovanni". The premiere was on the 29th October 1787, while Theresia was born on the 27th December 1787.
During the entire movie Mozart's piece "Eine kleine Nachtmusik" is mentioned and played. While it was indeed finished in 1787, the year of the story, it is still uncertain if it was ever released during Mozart's life. The first printing release of the piece came out in 1883. So it is very unlikely that the characters could have heard it.