When Abigail and Orville are rushing back to the farm, the backdrop is of an open road. When Abigail shouts for Orville to look out, the camera pans out to reveal that they were driving through a town.
Very early in the film Jane is upstairs singing while she is getting dressed. She sits down to put on her shoes and socks. The shoes are brown loafer style. When she heads down the stairs, the shoes are a black heeled boot style.
During the "Newspaper Dance" Gene Kelly wads up a full sheet of newspaper, drops it, then kicks it. It lands near the risers to the right of the frame. It is still there when he dances up the risers. In the next scene it is gone as he walks past where it was.
When Jane and Joe are in the barn dancing the "Portland Fancy", there are a bunch of onlookers in the background near the band stage. But when it cuts to a shot of Jane and Joe completing a dance turn, some of the onlookers have disappeared.
When Esme is washing the dishes the first morning with 'the crew' helping with the chores, in the long shot she reaches up to the shelf to add more soap flakes to the dishwater, and is shaking the box over the water. In the next shot her hands are both submerged in the soapy water, no box to be seen.
During the "newspaper dance," it can be seen the papers are printed only on one side, indicating that something other than newsprint stock was used, probably a heavier bond paper that was scored to allow for the clean tears.
(around 1 hour, 46 minutes) When it cuts to a two-shot of Esme and the sheriff standing off stage, the sheriff is laughing and talking to someone off-camera. This is a mistake. Apparently, the actor playing the sheriff was caught off-guard and unaware that the action had already started because when Jane and Joe enter the scene, the sheriff looks surprised and returns to his nonchalant grumpy character.
In the opening scene when June gets out of the shower, she puts on her clothes and her shoes. However, her feet are dirty. How could her feet be dirty if she just just got out of the shower?
In the "Friendly Star" number, as Garland finishes the song, the frame clearly freezes for a second before cutting to a shot of the moon.
At the beginning of "Wonderful You" you can see the shadow of the camera move across Garland and Kelly.