Okay, at the end of the first movie, Harry gets rid of his badge and is clearly not a cop anymore. However, in the sequel, he is still a cop working in the force, as though nothing had ever happened. Would someone like to explain that?
Magnum Force opens with Harry on loan to Stakeout, so maybe he was demoted as a result of his actions during the first film. Or for losing his badge.
Chances are that Harry threw his badge away in a moment of anger. On his long journey back to the precinct however, he likely had time to consider his actions and realize that for as pissed off at the law as he was, if he wasn't around to occasionally bend the rules then the bad guys would have an even easier time. When he got back he probably just said that he lost his badge during the long chase and fight with Scorpio.
At the end of the first movie, Harry saves a kid from Scorpio. After Harry kills Scorpio, he throws his badge into the water and walks away from the lake. Where did the child go? He is not seen in the wide shot of Harry before the credits. In fact it appears that after he falls away from Scorpio he vanishes completely.
Doylist: it was a continuity oversight, or the editor/director felt including the kind in the shot was unnecessarily distracting from the moment. Watsonian: the kid booked it out of there so fast after Scorpio was shot in the shoulder, he was nowhere in the area by the time the wide shot showed up.
What happened to Sunny from Magnum Force? We don't see Harry and her break up, and the last we see of Sunny, Harry tells he to stay in her apartment just before the climax of the film, but she never appears nor is mentioned in The Enforcer. And for that matter, what happens with Harry and Jennifer? It's implied that they start seeing each other (as Clint Eastwood and Sondra Locke were domestic partners at the time), yet again, she isn't seen or mentioned in The Dead Pool.
Probably as if Harry settles down with someone he'll stop being Harry and also in context of the film maybe Harry's true love was his wife or that he doesn't want someone to settle down with him as they'll be targeted as retribution from all the criminals he's done in.
In the first movie, how does Scorpio get his hands on that armory he apparently has? He's so poor he has to live at Kezar Stadium, and that rifle and MP-40 would cost some serious money, even on the black market.
Maybe he can indeed afford to live somewhere else, but he chooses to live at the stadium because he wants to spend all his money on weapons?