The directors--or, rather, two actors playing the directors--reveal at the end of the film how the physical comedy was done. Similarly, in real life The Three Stooges went on television several times, after incidents of children hurting each other while imitating the Stooges' eye-poke, head slaps, etc., to reveal how to eye-poke without hurting anyone.
During the 'dentist' scene early in the movie, the three boys claim to be 'dabbling in the arts' when Mother Superior comes into the room to summon them to lunch. Two of the three are doing things that mirror interests in their lives. Moe is reading something (according to his brother Jack) he loved to do. Larry is playing the violin which he was been quite proficient on (initially the violin training was in response to a childhood accident), indeed good enough his parents seriously considered sending Larry to Europe to study at a music conservatory.
In this film, Craig Bierko has a large mustache and works with a woman named Lydia. This is a direct reference to Groucho Marx of The Marx Brothers, a comedy trio that made films around the same time as the real three stooges. Marx wore a greasepaint mustache in most of his films and performed the song "Lydia the Tattooed Lady" in the film At the Circus (1939).
The actors in this film are much taller than the actual stooges. The real Moe and Larry were both 5'4" and the real Curly was 5'5". Chris Diamantopoulos, Sean Hayes and Will Sasso are 5'9", 5'11" and 6'3" respectively.