Before Casey's first skating competition, when Tina is standing outside of the car, she's talking about the CDs she'll play on the way back. At one point, she says "your music," but her lips are saying something different.
Casey's explanation - when she is making her video with her friend - is incorrect. She spins faster because of conservation of angular momentum. By pulling in her arms, she decreases her radius, thus decreasing her moment of inertia. Thus, her angular velocity increases - i.e., she spins faster.
In the opening scene Casey is skating on an outdoor pond (later revealed to be in Connecticut) wearing warm clothing and even a hat. A pond in the Northeast might be frozen between November-March. In the next scene, her teacher is suggesting she work on a physics project over the summer meaning it is around May or June.
In all the shots of Casey between putting on the outfit her mom got her for the Harvard alumni tea and arriving at the tea, the portion of the skating costume covering her hand isn't visible. When she reaches for an hors d'oeuvre, however, that portion of the costume is clearly visible.
There are many times during the mid-end of the movie where you can see a microphone hanging from the edge of the screen. (In those scenes, the microphone is covered by a black, furry microphone cover.) There is also one scene where the pole of the microphone is easily seen.
Casey Carlyle, who lives with her mother in Connecticut, goes to a skating competition in Pennsylvania, leaving her disapproving mother at home. Mom has a change of heart, leaves home after the competition starts, drives 200 miles and arrives in time to see her daughter skate.
Snowplow Sam skills are: sitting and standing, marching in place, marching forward, gliding, dips, backward wiggles, swizzles, rocking horse, two-foot hops, forward skating, forward one-foot glides, and snowplow stops. The Snowplow Sam class is learning advanced skills. During the practice session, the skaters are landing axels, which are usually learned much later.
When entering sectionals, Casey is not allowed to enter due to the fact she is in 5th place, since 4 are only allowed to take part. Five people are mentioned to be taking part in sectionals at the near end of the film.
At the party when Casey has figured out that the boy will swing through the window (and he does), as he goes through the wooden frame there is no breaking or shattering of glass as there would have been if break away glass had been used in the scene.