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.
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 is 18 in the movie, which means he is 18 when he dies. Since baby teeth are usually replaced by the age of 13, they shouldn't contain Jack's memory of the day he died. However there are instances when people may still have a baby tooth into adulthood.