The Oktoberfest scene at the beginning of the film was not staged. The filmmakers hid eight cameras to prevent people from knowing they were being filmed.
Sam Waterston arrived late to begin filming because his role in La puerta del cielo (1980) ran much longer than anticipated. By the time he began his work as Cutter he was exhausted. As a result people mention how awful he looks two times, and he blames jet lag.
The U.S. State Department issued several "real" passports for Matthau's character's several aliases. The documents were filmed in tight close-ups and were kept in a safe at the production company's office for security. When filming was complete, they were returned by hand to the State Department.
Glenda Jackson was reportedly delighted at the prospect of re-teaming with Walter Matthau after having co-starred with him a couple of years prior in the romantic comedy House Calls (1978).
The silver marksmanship trophy on Myerson's desk is always pointed at someone. When he goes after Kendig, it is pointed at Kendig. When Kendig gets back at Myerson, it's pointed at Myerson.