In M, there is a shot where Peter Lorre is being chased by the mob, and we see a pair of hands reach out and shove Lorre down a flight of stairs. The hands were Lang's own, and the look of betrayal in Lorre's eyes is because he was not told that the director was about to shove him down a flight of stairs.
John Ford, watching a scene in "Western Union" where Randolph Scott tries to burn the ropes off his bound wrists: "Those are Randy's wrists, that is real rope, that is a real fire."
In Fury, for instance, he wanted the protagonist to be guilty of the crime the lynch mob attacks him for (which would have been suspiciously similar to M), but a sympathetic criminal protagonist wasn't allowable under the Hays Code. Spencer Tracy's climactic speech was originally much longer and angrier in its condemnation of lynching.
Metropolis was famously eviscerated from 153 minutes to less than 90 by Paramount.
Hangmen Also Die! originally ended with the Nazis executing their Czech hostages, including a major character, and later survivors visiting their mass grave. This ending was finally restored in a 2014 video release.
Cloak and Dagger ended with a strong condemnation of nuclear weapons. Possibly under government pressure, this scene was cut and later destroyed by the studio.
Production Posse: Between 1921 and 1933, whatever Fritz Lang did always included Thea von Harbou as the screenwriter and, with only two exceptions (Peter Lorre for M and Fritz Rasp for Woman in the Moon), had Rudolf Klein-Rogge playing the villain.