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.
Anti-Sue: Ignatius J. Reilly approaches this, as he is basically a collection of any and all negative personality traits that cannot directly result in one's arrest. However, he is a deep enough character that he manages to avoid this.
Black Hole Sue: Wherever Ignatius J. Reilly goes, the world warps around him, and not just because of his enormous mass. Myrna tends to have a similar effect.
Idiot Plot: Most of the people in the book have a difficult time thinking rationally for extended periods of time, though this becomes doubly true any time Ignatius is around.
Iron Woobie: Mancuso. No matter what is thrown at him, he doesn't back down. Fortunately, it works out for him in the end.
Jerkass Woobie: Reilly is perhaps the prime example of a non-functional human being in modern society, but he doesn't deserve all of the bad stuff that happens to him. Indeed, the more naive reader might at first mistake him for just another "sensitive" young Sixties activist - one who's a bit strident, but definitely well-intentioned. However, this characterization is undercut by the fact that Ignatius is only getting involved in social causes to stick it to his holier-than-thou girlfriend.
Mr. Levy himself feels sorry for him.
One True Pairing: Myrna and Ignatius are pretty much destined to get together from the get-go.
Squick: Anyone who stands still long enough will get a lecture on Ignatius' valve. When it closes, he tends to fart and belch a lot.
Values Dissonance: As this was written at the height of the Cold War, there is obviously a little bit of this.
In the end, Lana Lee is arrested for distributing pornography to minors, which is treated as her just deserts. She deserved punishment, but not just for that.
Toole paints his characters in very broad strokes, mining New Orleans stereotypes to their fullest in a way that would be considered insensitive today. Burma is a pot-smoking, sunglasses-wearing, Jive Turkey-spouting black man. Dorian Greene and his retinue of Camp Gay men and Butch Lesbian women are another example. However, Toole is going for Rule of Funny rather than putting anyone down.
Values Resonance: In the beginning, Ignatius goes into a rant on how corrupt New Orleans has become, listing off all the vice and crime going on there. In among things like drug addicts, prostitutes, and gamblers, he lists "sodomites" and lesbians. Of course, arch-conservative that he is (or thinks he is), he would probably say the same thing today. Part of this is because Ignatius is supposed to be an Unsympathetic Comedy Protagonist who thinks civilization took a wrong turn at the Renaissance, so having his views become slightly more out of date doesn't really change his characterization at all.