The real Christine Jorgenson didn't wear female clothing when she was a child. In fact, she didn't wear female clothing until after she received her revised passport under her new name.
The movie is supposed to take place before, 1952(the year George becomes Christine) but yet people are using modern slurs to describe homosexuality. In reality none of the words used were common to describe homosexuality (at the time) example calling a man, "gay" in the 50s gay meant happy, the word queer meant, "strange or out of the ordinary" making this very historically inaccurate.
During a playground football game set during the Depression, a late-1960s car drives by in background.
The mailbox outside the cabin (in Denmark) is a typical US-style mailbox, not used in Denmark. Also, the address on the mailbox is "17 Skovsti". However, in Denmark, the house number comes after the street name, so the address should have been "Skovsti 17".