Continuity mistake: When Belle is watching TV at the Storybrooke hospital, her hair, hanging in front of her shoulders, changes position between the wide shots and the close-ups. (00:10:20)
Continuity mistake: At the airport, while Emma is standing in line at the security checkpoint, the way her red scarf is tied around her neck changes a couple of times, and the creases in the scarf repeatedly change between shots. (00:16:00)
Continuity mistake: When Anton is trapped in the hole, right before Charming exits his car, there is a shot of Anton clinging to the pipe, where you can see the rope they will use to rescue him, dangling next to him; even though the rope hasn't been lowered down yet. (00:20:40)
Continuity mistake: On the plane, Henry is eating baked goods from Cinnabon's. The size and position of the stains of frosting inside the box changes after he says "The only thing that could make this day any better, is more frosting." (00:40:25)
Answer: He knows who she is because he knows that the fairy tales are true. He was also shown to sneak out to go see Emma or someone else. Sometimes he succeeded, sometimes he didn't. This is how he knew to look for her despite his strict mother.