When the Man in the Moon communicates to North to identify Jack as the new Guardian, the moon is full. One day later when viewing the moon from North's home, the moon is clearly 3/4 full. Way too much has disappeared over a period of 24 hours.
When Tooth punches Pitch near the end, there are five tooth fairies hovering by her shoulder. However, the scene switches and she is not shown for a moment. When the scene switches back, only one tooth fairy, presumably Baby Tooth, is with her. As the scene continues, the number of fairies with her continues to change, first to eight, then to none, then back to five.
When talking about the egg hunt, Jamie and his friends say it's on Sunday. However, on the banners in the street (visible when Jack and Sandman are talking to Pitch) it says that the egg hunt is on Saturday.
Every tooth collected by the Tooth Fairy has roots, like a pulled adult tooth, but most of the teeth are supposed to be baby teeth, those that have wiggled loose after being displaced by permanent ones. They should be hollow shells without roots.
Jack Frost should not be able to carry Sophie home since it was ambiguous as to whether or not she believed in him, and was clearly shown in the beginning of the film that he simply vaporized through his non-believers.
When the guardians decide to help Tooth collect the remaining teeth after Pitch kidnapped all the fairies, they encounter a tooth-mouse (from the European division). If such divisions exist, having the fairies kidnapped would not have been such a big deal since the job was clearly still being done.