Continuity mistake: When Emma and Hook kiss, in the shots from behind Hook, Emma tilts her head to the right. In the shot from behind Emma, she tilts her head to the left. In addition, Emma's left hand jumps from the back of his head to his shoulder between shots. (00:37:10)
Continuity mistake: When Killian rallies his crew to join him in taking over the ship and becoming pirates, as he's holding onto the ropes used to control the vessel's sails, the number of ropes he's grasping repeatedly changes between shots; in some shots, it's only two ropes, in other shots, there are three ropes in his hand. (00:38:50)
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.