When the concierges are pulled away from their important duties, one concierge is administering modern CPR, which was invented in the 1960s. Promotion for non-medical professionals started in the 1970s.
In one scene in the elevator, the operator holds the control handle in its mid position and the elevator is rising. That position is "Stop." The next scene in the elevator shows the control all the way forward, which is "Up" and is correct.
When Jopling throws the companion Persian cat of Deputy Kovacs from a second floor window, the chances of the cat walking away unscathed (or with only minor injuries) from its landing tend strongly towards 100%. In what urban veterinarians have characterized as Feline High-Rise Syndrome, cats are now known to orient themselves four-paws-downwards within the first metre of falling (using their feline righting reflex), to spread out their legs mid-fall to maximize aerodynamic drag and thereby minimize falling velocity, and to arch their flexible spines just before landing, the better to absorb and harmlessly dissipate their kinetic energy on landing through muscles and skeletal joints.
When Jopling was in the gas station, the calendar on the wall showed "October 1932". The calendar was wrong since it showed October 5, 12, 19, and 26 were Sundays. In 1932 these dates all fell on Wednesdays.
When deputy Kovacs is trying to escape Jopling, he boards a bus and draws the shade down. This reveals the reflection of Jopling on his motorcycle. When Kovacs raises the shade, you can still see the reflection of the bike, but when the bus begins to move forward, the reflection of the parked bike moves along at the same speed of the bus. It should in fact remain in one place while the bus moves out of the frame (ie: POV of camera is stationary).
The goof item below may give away important plot points.
It is not possible for all of the events attributed to "October 19" to have happened on the same day. We hear that Madame D was murdered in the early hours of Oct 19, but that M. Gustave arrived "24 hours later". Then it is still Oct 19 after quite a bit happens, and he leaves.