Continuity mistake: Belle is talking to Rumplestiltskin and sitting on his dining room table. The red rose in the vase he gave her keeps moving. It is leaning to the right, to straight up, then to leaning to the right again. Neither of them touch it, so it should not be shifting around.
Revealing mistake: As Moe French steps out of his florist's van, he is greeted by Mr. Gold and his lackey. As. Gold says, "Well, this is just perfect", in the background, you can see the clock tower building, but without the clock tower (the actual clock tower is CGI). (00:03:50)
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.