Revealing mistake: In the opening scene right after she's put in the truck, she is lying on the bed looking in a mirror above her and her earrings are hanging parallel to the ground as though she was standing. (00:02:12)
Factual error: Frida is shown watching King Kong when she goes to New York. It is well known that the movie was made in 1933, but later we see on her mother's grave that the year is 1932.
Factual error: There is a reference to Happy Rockefeller in 1933 by Alfred Molina. She became Nelson Rockefeller's wife in the 1960s and was unknown at the time.
Audio problem: After Frida comes back to New York City from visiting her mother, she greets Diego. In the far shot her lips don't move at all.
Answer: The Song Frida is singing is one of Diego´s most favourite songs, La Bruja (On the soundtrack performed by Lila Downs). http://www.musicbrother.com/index.php?page=song&id=167156 (german page, but spanish lyrics).