In the film, Moe is in charge of the seed money. In reality Moe Howard would keep track of all of The Three Stooges' finances--Larry Fine liked to play the horses and Curly Howard would spend much of his money on women, so Moe made sure that some of their money was invested for when their careers ended. Moe himself retired a wealthy man.
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 the real Stooges' lives. Moe is reading, something (according to his brother Jack) he loved to do. Larry is playing the violin, at which the real Larry Fine was quite proficient (initially the violin training was in response to a childhood accident), indeed good enough that his parents seriously considered sending him to Europe to study at a music conservatory.
The movie is split into three episodes, which have an introduction much like the Columbia Stooges shorts--a picture of each Stooge along with the name of the episode and with the same opening theme song.
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. Groucho wore a greasepaint mustache in most of his films and performed the song "Lydia the Tattooed Lady" in 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.