After from the first game, Parappa lives in a place called Parappaville, which is (presumably) named after someone else. Considering that people who have cities named after them tend to be people of importance, perhaps part of the main character's obsession with proving himself is tied to sharing a name with this person.
The noodles Parappa won at the beginning of the second game are labeled "Beard Noodles." Which, given that Colonel Noodle is the Beard Burger Master's son...
Chop Chop Master Onion is a rap master with the head of an onion. He's a rap scallion.
In the last chapter of the first game, we see that General Potter is pretty quick to trust Parappa with his daughter despite seemingly trying to intimidate him just a moment before. Considering that he's close friends with his father, Mr. Parappa, there's a good chance he's known Parappa for his entire life and already knew that he was trustworthy. He probably just felt that it was his duty as a father to at least make the token effort to appear stern.
In the stage 3 cutscene of the first game, Parappa's shown driving his dad's car off the side of a mountain and landing with no damage to it. Moments later, he collides with a truck and THAT causes it to wreck. This seems strange unless you really look at the car during the collision: The impact launches the car into space for a moment, the car lands back on earth, THEN it falls apart. The crash wasn't what wrecked it. It was the fall from space, which utterly dwarfs a fall from a mountain.
It's only missable because of how catchy the song is, but when you think about it... how could Prince Fleaswallow work in the flea market when his mother was a baby?
It's probably a way of saying that his family has been working in the flea market for generations.
And then there is the fact that a DRIVING INSTRUCTOR forgets to close her car door.
I always interpreted that as one of Fleaswallow's lies. He is, after all, a con man. Lying is a part of his job.
The people of PaRappa Town are so ignorant, that FIVE of them saw Lammy get killed by a banana peel and NONE of them bothered checking her for life signs. Unless you're playing the American version.
