In the movie, Frida Kahlo, the wife of Diego Riviera appears. But Frida was born in 1907, so in 1920 she would have been 13, while in the movie she is portrayed as an adult. She married Diego only in 1929.
When Jeanne and Modi dance in the street, they are dancing to "La Vie en Rose" by Edith Piaf, which was not popular until the 1940s. Piaf was born in 1915.
On several occasions in the movie we see a bronze statue of the French writer Balzac. Near the end of the movie Modigliani is dancing in front of it. It is a sculpture made by Rodin. The movie is set in 1919, yet the bronze version of this statue was not placed in Paris until 1939. Rodin made it in 1898 and a full plaster cast was made and displayed. Yet it received much criticism and was removed.
In 1892 when Amedeo's mother is in labor the bailiff makes announcement that family's possessions are confiscated for the benefit of Republica Italia. At that time Livorno is part of the Kingdom of Italy - the Republic of Italy is declared after the WWII.
At the end of the flashback to 1892, there's an electric plug, which was invented by Harvey Hubbell in 1904.
Maria Tanase couldn't have had written one of the songs at the time the movie takes place, since she was a child.