Factual error: The USA map is inaccurate for the year it is set in. It shows all states but in 1886, many of the northwest states (e.g. Montana, Idaho, the Dakotas) weren't states until 1889+.
Factual error: A blunderbuss is fired at a safe. The shot not only bores a hole into the safe but also blasts it out of the window behind it. First, a gun can do no such thing; a cannon can. (The film already establishes that the safe is incredibly heavy.) Second, the hole on the safe is wrong. It is gouged outward as if by an explosion from within. (00:38:10)
Answer: 1886. The Statue of Liberty began being reassembled in April 1886 and was completed in October 1886.
Bishop73