Continuity mistake: After Charming gives Rumpelstiltskin his cloak, the cloak keeps changing position on Rumpelstiltskin's table. (00:22:05)
Revealing mistake: At the end of the episode, when Emma goes to Gold to ask for his help, we can see he's wearing a wedding ring on his left hand in addition to the usual ring with the light blue stone he wears on the right. That's actually Robert Carlyle's own wedding ring; as he wrote during a twitter Q&A session, he forgot to take it off before they started to film. (00:40:35)
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.