Character mistake: When Anastasia has to make out the 5 million dollar check to "cash" to get the money to release Mia, she signs the check with her old last name, "Anastasia Steele" instead of "Anastasia Grey", which is written on the top left corner of the check.
Suggested correction: A key point in the movie is how Christian is upset that she didn't take his name in her work life, so it wouldn't be unreasonable that she signed the check using her maiden name (it also could have been just as easily a force of habit thing, it does take time to get used to using the correct name!).
Character mistake: The tour guide inside the "Degenerate art" exhibition ridicules the 'child-like' paintings of the likes of Mondrian and Kandinsky. In particular he stands in front of Kandinsky "Upward." The German name of the work is "Empor", but the tag says "Empore." (00:03:40)