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.
Is the main character a Well-Intentioned Extremist out to clean up Saints Row and protect it from evil corporations or is he a Crazy AwesomeHeroic Comedic Sociopath out for himself? Some combination? The ending of 2 shows that The Boss just wants power and money, and all the benefits of those. The multiple endings and add-ons blur it further. In one ending Boss descends into cartoonish supervillainy, in the other s\he's better. And in Gangsters in Space and The Trouble With Clones Boss is practically heroic.
Also, were they always like that, or did the explosion at the end of Saints Row give them brain damage?
Julius. Good or evil? Julius's motivations never change. He's always trying to clean up Saints Row. However, his methods of doing so actually don't stand up to close scrutiny. After using the Saints to wipe out the other gangs, Julius decapitated them and turned them over to the police. Even if you think this gross act of betrayal was warranted, he just made a power vacuum for other gangs to fill.
It gets worse. Julius actually didn't intend for there to be a power vacuum. He'd made deals with the Columbian drug cartels and did things the Vice Kings never would have done under King's leadership. He only betrayed the Saints once the police took him into custody.
Was Cyrus Temple just an evil psychopath along with his lover, KIA, or did they go crazy because of a combination of the Saints continued popularity mixed with the deaths of hundreds of STAG soldiers?
Continuity Lockout: Stated to be the reason that Volition didn't follow up on the Ultor story arc and Dex after the "Ultor Exposed" DLC trilogy; they didn't want to confuse potential new players or alienate the ones who weren't able to play it. Which is somewhat baffling, as Saints Row IV is pure, undiluted Continuity Porn and references characters and events from the series all the way back to the first game (which, mind, was exclusive to one console, so a huge chunk of the fanbase has never played it), but beyond a single throwaway line early in the game, neither Dex nor his betrayal are ever addressed again. However, Dexfinally returns in the add-on Gat Out of Hell, meaning someone at Volition must have noticed the massive Fridge Logic wrench that SRIV dropped into their original explanation about alienating new players.
Ensemble Darkhorse: Johnny Gat, Maero (to a lesser extent), Matt Miller (enough that he was brought back in IV), Kinzie and Shaundi.
Fanon Discontinuity: Some fans of the first two games disregard the third and fourth, for a degree of Reverse Cerebus Syndrome, and feel that they (the fourth game espically) take the Saints away from their gang roots.
In the second game Shaundi was voiced by Eliza Dushku, and in the third game it's mentioned several times that she really hates the actor who plays Nyteblayde. Given one of the influence of the character this is amusing.
Jerkass Woobie: Given the nature of the game Shaundi fits as well as someone in a more serious work. After a bad spring break where it's implied she worked for a pimp she was on the path to drug hazed oblivion until Gat and Boss recruited her, who she looked up to. She then becomes really torn up at Gat's death, it turns out she has nightmares over being kidnapped and blames herself for not being better, for Boss and Gat feeling they have to protect her rather than her protect them.
Rated M for Money: "Blood and Gore, Intense Violence, Partial Nudity, Strong Language, Strong Sexual Content, Use of Drugs and Alcohol." It's not really a game meant for kids.
Sacred Cow: The second game is often viewed as this.
Scrappy Mechanic: In the first two games, the Respect system would halt storyline progression until enough levels of respect are gathered to use like expendable "credits" for unlocking plot-based missions. While earning respect isn't all that difficult, it's still something of a pain in the ass for players who want to just jump right into the story. Parts 3 and 4 remove this particular restriction.
That One Sidequest: The dang Insurance Fraud quests, where you have to gather money by getting hit by cars. The best way to do so it to start a long chain of getting juggled, because a multiplier is added to each hit, but good luck with that, because cars tend to be either rare in the designated areas or they're moving too slow or fast to effectively start the chain and steer into them.
Insurance Fraud activities are significantly less painful as of The Third, with more and faster-moving cars and a larger designated area allowing you to easily seek out heavier traffic. IV made this easier with Superspeed and hitting the triggr buttons. In some points, you end up being flung across the map if you get hit by a garbage truck, a bus or a speeding car which can rack enough money while your character is having This Is Gonna Suck comments.
"Heli Assault" and "Guardian Angel" take its place as the major pain-in-the-ass activities, the former for being an escort mission where you fly a chopper (with their notoriously floaty controls), the latter for being an escort mission where you ride in one, but are stuck using only a rocket launcher to fend off enemies, which has a tendency to accidentally kill your homies via splash damage.
Another would be the escort missions, as you can't fight back against the newsvans, only hope to drive faster than they do.