The movie's most inflammatory sequence is not Harry's famous, twice-delivered "Do you feel lucky? Well, do ya, punk?" monologue. It's the scene in which Harry traps Scorpio and then tortures him to learn the whereabouts of his latest victim (who, unbeknownst to Harry, is already dead). "Rights. … I have rights," Scorpio shrieks, sniveling as Harry's foot presses down on his bleeding leg. Because of Harry's literal overstepping, the killer eventually goes free; he then hires a large black thug to beat him up so that he can work the easily duped court system by filing a false police-brutality claim. While the city's brass wants to bargain with Scorpio, Harry knows the only solution is to hunt him down and kill him. Which he (spoiler alert) does.
In other words: Of course this is a right-wing fantasy. Ideologically, Dirty Harry was a well-calculated sop to the group of Americans that Richard Nixon identified in 1969 as the "Silent Majority" (though neither word was entirely accurate), those for whom everything about the period, from burning ghettos to women's lib to anti-war marches represented steps toward barbarism.
Harris fails to mention that the torture of Scorpio was a "ticking time-bomb" scenario. Scorpio had kidnapped a little girl, ripped out some of her teeth and mailed them to the police as proof that he had her, and had stashed her somewhere. Harry thought the only way to save her was to torture Scorpio. Was this justified? I thought it was interesting cinema, because the main character had to make a choice between the law and the life of the girl.
And then Harris leaves out the very end of the movie. After Harry kills Scorpio, what does he do? He throws his badge into the water. There are multiple ways to interpret this action, but I think one clear implication is that he realized that he couldn't function within the confines of the law and still be true to the people he vowed to protect. If this makes Harry fascist, then what does that make Batman look like?
Another significant ommission of Harris' is the fact that in the original movie Harry never kills anyone who isn't either holding a weapon or making a move for a weapon. He doesn't indiscriminately blow bad guys away. He gives them a choice, to gamble with their lives by picking up a weapon to kill him, on the chance that Harry's gun is out of bullets.
The implication of the films is that the system has become bloated and bureaucratic to the point where it protects criminals more than citizens. In that sense it's reactionary. But the character isn't an assassin with a badge. He's more lawful that most movie superheros, and he's at the other end of the spectrum from Bronson's character in Death Wish.
He's just a decent guy with a giant hand cannon trying to protect the honest, hard-working people of San Francisco.