The first occurred right after the scene with Potter in the meeting of the board of directors after Peter Bailey's death. George was running out to catch a cab to the train station to go to college and start the rest of his life, when suddenly one of the directors runs out and tells all the employees that they voted to keep the Bailey Building & Loan open -- but only if George stays on as president. George freezes in his tracks and his face drops . . . and the camera zooms in on his face as he realizes that so many people are depending on him and he can't let them down.
The second occurred near the end of the movie, when George finally realizes that the "world" Clarence was showing to him was real. He runs out of the old house and down to the sidewalk, and for a moment he freezes in the darkness, staring at the camera with the wild-eyed look of a crazed man. This is the moment when it sunk in for him -- and he desperately needed to have Clarence tell him what had become of Mary in this world where he didn't exist.
In my opinion, those are the two most powerful moments in that film.
Pretty good observation, AC.