When Dr. Flammond tells Nick that the weapon has to be completed by September 24, Nick replies "That's Simchat Torah!" Simchat Torah is a festive Jewish holiday in which the liturgy includes reading the last portion of Deuterotomy, final book of Moses, and then beginning the cycle again with the book of Genesis. In 1984 Simchat Torah fell on October 18.
When the conductor speaks to Nick in German on the train at the beginning of the film, Nick translates that they're at the East German checkpoint. However, East Germany (The GDR) didn't exist until 1949.
When Nick enters Dr. Flammond's cell and Dr. Flammond is seen emptying spoonfuls of dirt from under his cot, you can clearly see him scoop dirt from a different pile underneath the cot rather than the tunnel he was nearly completing.
Chocolate Mousse (Eddie Tagoe) wears crossed belts of linked machine gun ammo, but all the cartridges are blank cartridges. This could be an intentional "mistake" since the difference between blanks and real ammo is so obvious.