Humphrey Bogart accidentally set his left thumb afire with lighter fluid while filming the scene in which his character burns some documents. The accident is visible in the film.
The opening scene in M*A*S*H (1972) pays homage to the one in Battle Circus complete with helicopter landing at camp.
The film originally had a different title but the studio and the director thought that title would mislead audiences, so "Battle Circus" was instead chosen. The original title that was rejected was "MASH 66." Both the film M*A*S*H (1970) and the TV series M*A*S*H (1972) depicted the 4077th Mobile Army Surgical Hospital in South Korea; MASH 8063rd was a sister unit.
The opening credits show the complete unit name as MASH 8666, Mobile Army Surgical Hospital, above the movie title.
This was Humphrey Bogart's only film for MGM. Like his films for Warner Bros., it is now owned by Turner Entertainment, which itself has been part of WB since 1996.