The acting troupe is a Badass Bystander group. They're obviously talented, given how they have to carry the show. In both movie versions the audience is hostile, with Max explicitly saying a mob will ensue, but The Show Must Go On. They stay in character even as the audience walks out, and when Hitler's actor saves the show.
Pulling off the "swastika dancing" scene on-stage. One of the best moments in "Springtime for Hitler" is the above shot where you see the dancers in a swastika formation. They simulated this on-stage using a large mirror and mannequins on dollies... and it worked.
The original movie
The scene where Leo decides to join Max Bialystock in front of the fountain at Lincoln Center.
Someone off-stage knocking out Liebland when he tries to hijack the stage and announce that it's gone beyond his intent.
Leo finally grows a spine and says one of the best lines in the musical. "And you're right, Mr. Marks! You are a CPA! A certified public ASSHOLE!" Followed shortly by the accountants cheering, "Hooray!"
The counterpoint duet sung in the taxi between Leo and Max.
"Stop the world, I wanna get on!"
In the film, Nathan Lane keeps singing while he plays the piano, grabs a flower for his lapel, throws his hat in the air, opens a door, and catches it without looking up, all in one take.
Uma Thurman is an actress not normally known for her musical talent, She not only holds her own against two Broadway veterans, but blows them both out of the water during "When You've Got it, Flaunt It."
Even more impressive as years later she revealed that she'd just recently suffered permanent damage to her neck and knees during a car stunt in Kill Bill.
The bum in the bar belting it out in a deleted scene. And said bum was played by Ernie Sabella.
"You've made a fool of Hitler!" "Well, he didn't need our help."
The deleted "Challenge Tap" where "Hitler" is challenged to a dance-off by the main world leaders: Stalin, Churchill and Roosevelt. Roger has to tap dance around all the three actors and show off his chops.
Without Peter Sellers championing the 1968 film, it would never have seen wide release.
Mel Brooks winning a Best Original Screenplay Academy Award for his very first movie screenplay. Also take into account how often comedies get Award Snubs on Oscar night, and how long it took The Producers to find its audience during its original theatrical release.
The absolutely massive Tony sweep. Not even Mel expected that big of a victory.