PJ is portrayed in a significantly more comical fashion in the sequel than he is in the first movie or the show. Is it losing track of one of the characters' narrative purpose? No, it's enhancing it. Because PJ's first line in the movie is winning a game of Misery Poker, we know they haven't lost track at all—but he is portrayed more comically because after the first scene (when he leaves home), he's free to joke.
It may come as a bit of a surprise that PJ seems fine with his weight, considering how little confidence he has about everything else, at least until Beret Girl asks him to dance. Well, what's likely to be the only trait he has that Pete has never insulted him for? The one that they both obviously share without close examination.
Roxanne's absence makes a lot more sense when you take into account the fact that she and Max dated as teenagers. Middle-to-high school romances are very often short-lived.
However, it is noted that we see Roxanne in one surprising place: House of Mouse. It was the focus of an episode and given Max went through his growth spurt, they probably dated for a few years before putting things on hold for college.
Bobby's growing importance from the first to the second movie makes sense when you examine his interactions with Max and PJ. Back in Goof Troop, Max was the optimist to the more realist PJ, balancing each other out. However, Max became more moody and lost confidence in himself as he entered his teenage years. Enter Bobby, who is a slightly obnoxious, but well-meaning and cheery sort of guy who helps bring a brighter spark to the duo and thus balance matters out. No wonder that he becomes close friends as he brings a new level of optimism and new way of thinking into their lives.
It's easy to interpret Bradley rejecting PJ and Bobby as Gamma prospects because he thinks they're losers or assumes unfairly that they don't have the talent to compete. But considering that the Gammas have always cheated to win, he may have, purely strategically, assumed that Max would be the most loyal. PJ's obvious discomfort would make him unlikely to go along with the cheating (and possibly even tell an authority) and Bobby being so unashamed, in contrast, would make him less likely to keep it under wraps even if they did convince him it was okay. In particular, Bradley saying "I thought you wanted to win" makes more sense from this lens given the cheating. They were accepting of Goofy because Goofy is liable enough to misunderstand situations that they didn't have to worry as much about either.
As the Lady at the unemployment office responds to a doubtful Goofy with "Dog, you're never too old to learn new tricks", what makes it fitting is that Goofy is a literal dog about to learn new tricks.
Goofy's change in jobs between movies is actually pretty easy to explain. He was fired from his job in the first movie for running out in the middle of the day and taking an extended vacation with no notice whatsoever and then spent all of his savings on the aforementioned vacation as well as replacing his exploded car. His depleted finances meant he had to take the first job he could get just to pay the bills. Once things stabilized, he couldn't get another, better job, because of his lack of a degree and he couldn't even use his previous employer as a reference because of how he was fired.
PJ goes through considerable Character Development after being asked out by Beret Girl... but if PJs confidence, self-esteem, and happiness skyrocketed after Beret Girl asked him out, that must mean he puts a lot of stock in her opinion. What's going to happen to him if she dumps him?
While Cartoon Physics prevent anyone from being seriously injured, the fact remains that Bradley has no qualms about using potentially lethal methods to eliminate the competition and just because nobody died this time, it does not mean nobody ever has.