When Lou Costello is mistaken for a male model and forced to strip, there is a very visible bandage on his right arm; that was to mask the bracelet containing the name of his baby son, who died in 1943, which the comic had welded closed so it could never be removed.
This was the first Bud Abbott and Lou Costello feature in which they did not play a team. The story centers on Costello's character, while Abbott doesn't appear until 16 minutes into the film. While many assume this was because the two were having a feud, it's only part true. While the pair did have a feud and weren't speaking, this was during the filming of Here Come the Co-eds (1945) and The Naughty Nineties (1945). The feud was over by the time of Little Giant. They realized that their popularity dropped after the release of the last two films, so a decision was made to try something new and focus on situation comedy instead the usual routines. This experiment was also carried out in The Time of Their Lives (1946).
This film was regarded as a major departure for Bud Abbott and Lou Costello. It was their first situation comedy, and the comedy was character/situation-driven rather than gag-driven.
Of all of the films that Bud Abbott made for Universal, this is the only one where he portrays a married man (although in the story, the marriage is kept secret).