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.
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.
George Guetary's character states that he is "strictly a three-quarter man". This is reinforced by the song "By Strauss". However, his later musical number "I'll Build a Stairway to Paradise" is definitely not in 3/4 time.
When Gene Kelly is painting Lisa'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.