After hearing that Brett signed a deal with a record company without Miles, Nora runs up the stairs upset to find Brett. Before she runs up the stairs her hair is curly and when she finds Brett and starts getting angry with him her hair is straight.
When they are standing looking over the bay, we can see the port on the other side. There is a large ship which is being loaded. After there is a close up of the two talking and they are about to begin dancing we see the cranes are up and the ship has vanished.
When Mac discovers Tyler is dancing at the school for the first time and they go outside, Mac's shirt is buttoned on the lowest button. It then switches to being buttoned on the second lowest button, and then back to the lowest button.
When Miles comes to take his laptop in the Dance Room, he has his laptop in his hands when leaving, after talking to Tyler. However, when Nora comes in with Brett to talk about finding her new dance partner, Miles' laptop is back again at the table in the background. A while later, his laptop is not there anymore.
When Nora is talking to Director Gordon about Tyler being her new dance partner, there are a few papers lying around on her desk. In the next shot, the paper is tidy. But after Tyler repeats himself as "adequate", her desk is back to messy again.
When Tyler is dancing in the last dance, after he lifts Nora he puts on a shirt and his hat. When he puts on his hat, the cap is turned to the left, one shot later the cap of the hat is turned backwards.
In the scene where Tyler goes to the Maryland School of the Arts to apologize to Nora before the ballet class, they are walking along the side of the school, but as they walk, they don't make any progress down the sidewalk. The scene was clearly filmed in segments that don't coordinate.
Tyler is eating with his foster family the day he is approved to rehearse with Nora. The logo on the cups and bags on the dinner table is for a fast food chain in the Western US. There are none in Baltimore, MD, where the movie is set. The nearest (according to the company's website) is in Oklahoma, more than 1,500 miles away.