Continuity mistake: The dove that Mary Margaret finds in the woods has white feathers with a reddish plume around its neck. When she releases the bird after the storm has passed, it is not the same dove. The dove that she releases is completely powder white, with a different colored beak. (00:12:20 - 00:29:40)
Continuity mistake: When David is talking to Kathryn in their bedroom, after Kathryn says "It's also been hard on me", the number of buttons that are buttoned on David's shirt keeps changing between shots, which can be seen from the way the opening at the top of his shirt keeps changing in size. (00:34:50)
Continuity mistake: At Granny's, the banknote that Archie puts on the table as he leaves turns around between shots. When Emma asks, "What about that drink?", the money has moved to a different part of the table. (00:28:10)
Continuity mistake: After Charming and Snow embrace in King George's castle, Snow's hand is on Charming's chest. In the next shot, it is resting on his shoulder. (00:32:45)
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.