The title "I've got a secret" is misspelled as "seacret".
Young Bobby Fischer said that he plays chess since 9 years old. Actually he started playing it when he learned it at the age of 6.
At the end of the movie it is said that the Bush Goverment decided to imprison Fischer for his game in Jugoslavia. However he wasn't in prison in the USA since Fischer didn't spend any time in the USA since 1992.
Misspelling "Adaption Agency" instead of "Adoption Agency"
Arthur meets Boris Spasski in Moscow present days (2009). However at that time he lived in France with his wife.
During the video interviews in the last moments of the movie the screen of the camera is closed which would mean the camera is not on and is not recording at all.
A moment in Russia supposed to set place in Moscow, as it can be heard by the "Kuranty" bells. However the columns of St. Petersburg can be seen.
During the meeting with Boris Spasski in Moscow in present days he is standing in front of a bookshelf with books only in English, not in Russian as it should be.
When Arthur is asked to write a book on Bobby Fischer he is asking "A biopic"? The term "Biopic" is usually used for biographical motion pictures, not for book biographies.