Dirty Harry is strong on Chaos ... meaning that he serves Law by any and all means possible, including illegal and unlawful ones (like torturing Scorpio in the sports field to find where he hid the body of the teenage girl he kidnapped, killed and raped, for example). The end (smiting evil) justifies the means.
Law believes that following the law at all times is the best way to spread good (sort of a rephrasing of Buddha: There is no way to happiness [goodness], happiness [or goodness, for this metaphor] is the way). The stereotypical Paladin will always follow the rules, even when evil may gain some advantage by this, notwithstanding. So even though a Paladin might come across a civilization of peacable undead creatures living in harmony with each other and their underdark neighbours, that Paladin must smite the undead no questions asked.
There is a difference between Good and Evil; you are struggling because there is no embodiment of pure good or evil in our reality. Causing hurt to others for no other reason that to gain some sick personal thrill is generally regarded as evil regardless of the perpetrator and victim, for example. (Read Zimbardo's latest book The Lucifer Effect, which is subtitled Why Good People do Evil for an excellent definition of evil, as well as a thorough discussion on the power of situation forces to affect individuals, especially in novel scenarios.)
Perhaps a useful way to examine the various facets of Good, Evil, Chaos and Lawfulness is by considering the mixed alignments, like Chaoric Good (the person who is prepared to bend the rules to gain the most good) and Lawful Evil (people who may be trapped into behaviours because they are rules).