As the ship leaves Hamburg, it's stationary in some shots and moving in others.
Just before the boat leaves Hamburg, the shots vary between daylight and night.
When the St Louis is towed from the Havana quay to anchor in the harbor (1:34:30), this triggers Carl Rosen to jump overboard. When he does so, the St Louis is clearly still attached to the quay with multiple stern lines (1:35:50-1:36:10).
In the film, the ship's hull is white. The real-life St. Louis had a dark hull.
A 1970s red London bus drives past the German Army HQ in late 1930s Hamburg.
Several actresses have 1970s hairdos.
'Besame Mucho' was written in 1940. 'El Cumbanchero' was written in 1946.
In a Havana street scene men are wearing 1970s tight bell bottom blue jeans/pants.
When the boat is at the dock, the players in the band at the quayside are clearly pretending.
At the beginning of the movie, the voice for Leonard Rossiter is dubbed very badly. His mouth movements don't come close to what is heard.
In some of the scenes set in Havana, Cuba, mountains are visible on the horizon. In fact, the environs of Havana are completely flat. The Havana sequences could not have been filmed in Cuba during the 1970s due to the US trade embargo, and the filmmakers chose a location (in Catalonia, Spain) in which mountains are visible the background.