"Fraulein, is it to be at every meal, or merely at dinnertime, that you intend on leading us all through this rare and wonderful new world of... indigestion?" "Oh, they're all right, Captain. They're just happy..." (cue mass bawling)
Kurt reprimanding Brigitta for calling Maria's dress the ugliest one they ever saw, since one of their previous governesses wore an even uglier one.
"Will father approve of this?" "Of course [...] Don't you trust me?" "No." "You're a very intelligent girl."
"So long! Farewell! Au revoir! Auf Wiedersehen!" "I'd like to stay and taste my first champagne! Yes?" "No." Liesl's pouting face afterwards.
It comes to her later: "KURT! That's the one I left out! God bless Kurt!" *BOOM*
When Kurt introduces himself as "incorrigible", Maria responds with "Congratulations"...which is funnier when you realise what incorrigible actually means (uncontrollable or firmly fixed in their ways)
Maria stops in the middle of her own musical number when she sees the size of the house. Julie Andrews's delivery of "Oh, help" is priceless.
Remember how Maria said nuns' worldly clothes are given to the poor when they join the convent? At the opening of the scene where Reverend Mother convinces Maria to return to the Von Trapps, she has just finished admitting a new postulant, and sends her to change into her robes. In the next scene, when Maria returns to the Von Trapps, she's wearing the dress that new postulant gave up!
After Liesl casually mentions that Louisa can make the climb up to the governess' room with a whole jar of spiders in her hand, Maria reacts brilliantly. Despite having a heart-to-heart with Liesl, she spends the rest of the scene sneakily checking under her bed clothes for anything. She jumps when she does find something... but it turns out to be a slipper.
Somewhat "meta" here, but hearing the nuns complain about Maria "singing in the abbey" becomes about five times funnier when you realise that this complaint is expressed through song, while they're in the abbey.
Brigitta's blunt honesty throughout the film is priceless.
When the children and Maria discuss who should sing next, Maria then presents her guitar to the Captain. The look on his face is utterly priceless.
The Salzburg Marionette Theatre premiered a puppet version of The Sound of Music in 2007. Among other changes, "The Lonely Goatherd" plays during the curtain call...in which the puppeteers operate marionettes of the Von Trapps operating marionettes of the characters in the song.