In the film, "Harold Hill" and Marcellus sing "The Sadder But Wiser Girl for Me" to Amaryllis (a child). Keep in mind that this is a song about Hill preferring more experienced women. Not exactly something suitable for a child, but Amaryllis loves it. Amaryllis's reaction of oblivious enjoyment to the song is probably meant to be a reflection of how most children will react to the song.
The townspeople fall for Harold Hill's Moral Guardians arguments over the pool table very easily. But considering how they feel about the books Marian recommends, Hill's claims fall in line with their Everyone Is Satan in Hell mentality. The one person in town who seems immune to his claims is Marian, who sees nothing wrong with those books and doesn't share that mindset.
When Marcellus (who used to know Hill) first sees Harold Hill in the film he calls him Gregory. "Harold Hill" quickly tells him to be quiet saying his name here is Professor Hill. The fridge part kicks in when you realize that by the end of the film he still hasn't revealed his (real?) name to anyone in River City. Of course he may reveal it after the movie but if "Gregory" is connected to any crime he may just try to continue in his new identity.
