These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Frank is usually treated as a absolute moralist who just happens to be fighting a never ending war on crime. Other interpretations imply he's just as bad as the monsters he fights and is little different from a serial killer. The only thing that stays the same is the reason why he became the Punisher.
Punisher: Year One has yet another take on Frank's character - he goes vigilante only after all other methods of bringing the mobsters who killed his family to justice fail spectacularly (the police is ineffective and corrupt; an attempt to do an independent investigation leads only to death of the reporter whom Frank briefly befriended).
Punisher: Born from MAX imprint has a different take on WHY he became the Punisher. Frank fell in love with killing and made a deal with an unknown supernatural entity (or just plainly went mad, you choose) to fight a war that would last forever. He wasn't informed until later that the price would be his family, at which point the supernatural entity makes Frank forget that they ever made the deal.
For instance, in an early appearance, he tried to kill people for running stop signs and littering (this was Hand Waved in The Punisher: Circle of Blood by saying he had been drugged by Jigsaw to make him more violent and hardline).
Frank and Microchip would come off like an old married couple sometimes. In some issues, Micro would even use the word "bubbelah" (Yiddish for "darling") when talking to Frank.
Franken-Castle's fight with Daken was filled with homoerotic banter.
Magnificent Bastard: Frank himself. Agree with his methods or not, but either way he is damn good in what he does. Just try to keep tally of the times where he got out of a seemingly impossible situation or pulled off a complicated plan to get to his target. Occasionally he even outsmarts super-powered beings far more mighty than him. What Reed Richards is to Science and Tony Stark to Mechanics, Frank Castle is to Warfare and Survival.
My Real Daddy: He's had a few writers over the years who have done well with the character, but in recent years the one that most readers will think of is Garth Ennis.
Sequel Displacement: While Frank was one of Marvel's cash cows back in the early nineties (alongside Spider-Man and Wolverine), many of his modern fans know nothing about his stories before Ennis. Sadly this means that a lot of his gentler characterizations are overlooked, as well as the fact that he actually did have something of a supporting cast.
Which is what a lot of fans said of Angelic Punisher.
Many people feared the worst at the announcement of Franken-Castle. Surprisingly, the change has been immensely popular. So much so that his ongoing series was renamed Franken-Castle for a little while.
Writer on Board: Garth Ennis hates conventional superheroes. You cannot help but notice that whenever any of them appears in an issue of the main Punisher series written by him.