When Barney and Lisa travel by train through Switzerland, the train, as seen from the outside, changes between shots.
The basic premise of the movie (that oil companies are hiding a "secret" formula for converting coal into gasoline) is false, as the formula is well known and has been known for a very long time. It's readily accessible.
When Barney and John leave a room, close the door and enter the corridor, we can read the shadow of the text on the door window on the opposite wall, "453 PRECINCT COORDINATES." However, the text should be mirrored since the door is illuminated from the inside of the room.
Just as Barney is about to board his plane to leave Germany, his German counterpart has to explain to a woman (in German) at the gate, about his trip and his needs. But after they find out the formula he was carrying is a fraud, Barney begins talking a rapid and agitated manner to the same woman. And now the woman not only seems to understand English very well, but she speaks it as well.
When Adam Steiffel and Barney Caine are walking and talking Steiffel says he has to walk on the right because of the bad hearing in his left ear. Despite having a hearing aid in his left ear, he would naturally walk on the left side of Caine so that his good ear (right one) was next to Caine.
In his office when Steiffel is explaining things (the denouement) to Caine, Steiffel says he rather be in the mountains fishing of hiking. He's obviously morbidly overweight (as Brando was) and there's no way an avid hiker would be so overweight.
At the beginning of The Formula, a Nazi General is given the task of driving a truck to the Swiss border. In the next scene, the truck has been captured by the US Army. The scene is shot in the snow. This is supposed to take place April 16-19, 1945 as the Battle of the Seelow Heights is mentioned. There is nowhere that would be covered in snow between Berlin and the Swiss border at that time, even if he went the long way i.e. via Austria.