Big Mouth has a Shy Bladder
In "The Potty Problem", Big Mouth has to go to the bathroom (presumably Number One, since he'd just done Number Two recently), he didn't go until Peg and Cat sung a song, and then the second time, he did it while everyone was out of the bathroom. People with shy bladders sometimes use music to distract themselves. The Neighbor Ladies are a couple.
I mean, the two even have a photo of them together in their house. Though, if they were a couple, they might like stereotypes a bit less, as couples of the same gender are often stereotyped.- "Their house"? They don't live together.
Roxanne is Ramone's cat.
I mean, Peg is awed by Ramone because of his talents, and the same is true for Cat and Roxanne. Though admittedly, it's implied that Cat also has a crush on Roxanne, whereas Peg is just impressed by Ramone's talents like 90% of the cast is. Their names even both start with "R" and end with "N-E". Peg actually is allergic to all clovers; not just four-leafed ones.
The one under her hat just happened to be four-leafed.