We see Adam in his studio three times. When we first see him, alone, he is playing a black baby grand. The second time, he is playing a brown baby grand upon which Jerry dances. In the third Adam studio sequence he is alone, again, playing the black grand. Perhaps the brown piano was fashioned to accommodate and withstand Jerry's dancing on it.
Near the end of "S' Wonderful," the position of a green car changes between shots.
Shadow tracks across Henri while he is seated singing "'S Wonderful", as the camera begins to pull back.
When Jerry meets Milo in the street art market, the shadow cast by the wall jumps across the pavement from shot to shot until it is four feet wide, in the space of a moment or two in the story.
In the café before "'S Wonderful", the level in Henri Baurel's sherry glass fluctuates wildly between shots. Also, Adam Cook knocks over his brandy glass and it falls under the table; then it reappears, then disappears.
When Jerry and Lise walk down the stone stairs to the river for the first time, the sound their steps make indicates the stairs are really made of wood.
When Jerry and Lise walk down the riverside together, Jerry leaves his coat by the tree.
In the "By Strauss" waltz, Jerry is dancing with two ladies in the café, and his cap falls off while he is kneeling. He briefly attempts to retrieve it, then leaves it where it is.
When Gene Kelly is painting Lise's portrait, she poses with a red carnation in her hand. When they lean in to embrace the carnation falls on the ground and is momentarily out of view. He bends to pick it up, but it's no longer a carnation but a red rose. The difference is quite obvious in the flower petal arrangements.
In the same scene, the aghast Adam Cook brings his coffee to his lips without removing his cigarette and dunks it, but puffs of smoke continue without pause.
When Jerry, Henri, and Adam are performing in the café, a flower pot on top of the piano moves around between shots.
Just after the "Our Love is Here to Stay" dance Lise rushes off to met Henri at the stage door. Henri introduces her to an American producer who has invited him to perform in America. As soon as the producer leaves, Lise starts to apologize to Henri for being late. If you listen very closely, you'll notice that she starts speaking in French ("Je ....") She immediately catches herself and continues in English, "I'm sorry." Since both actors were Francophones, in real life they would naturally have conversed in French.
After the ballet, when Jerry bends down to pick up the rose on the grown, the shadows are inconsistent between shots.
During the ballet dance sequence just before the girls are all on their toes, Lise is in the background with Jerry...then in an instant appears in the front of the scene with most of the other dancers not showing as she waits for him.