Dirty Harry/Headscratchers

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.
• Simply throwing his badge in the river does not mean he stops being a cop. He would actually have to go to Police Administration and file his resignation to do that. If Harry changed his mind about quitting in-between the badge-throwing and actually going back to the precinct building, he'd still be employed. (He'd also have to account for losing his badge, which is a disciplinary offense in most police departments, but its not like Harry isn't used to getting his ass chewed out.)