Reggie's jerkassery has become something of an Informed Attribute over the years, as his character has definitely softened and become more sympathetic while characters (including himself) still describe him as "Rotten Reggie". It has gotten to the point where many readers consider Reggie to be the everyman who represents teens as a whole instead of the JerkassProud Elite.
Also, his obsession with Archie. Some fans believe he is in love with Archie but hiding it. Others insist that every action Reggie takes towards him, no matter how violent or cruel, is actually his reaching out to Archie in his own twisted way. It is hinted in-series that Reggie is jealous of how Archie is loved by everyone for who he is while Reggie has to put on a strong front.
Believe it or not, arguments have popped up surrounding Betty: Is she a Housewife/Proper Lady in waiting (pro) or a Yandere in waiting (con)? This article from MightyGodKing is definitely in the Beyond-Yandere column. A large portion of this is due to Characterization Marches On. Note that a few older stories have Archie intimidated by her, as she reminded him of a cat about to pounce.
Why exactly Betty and Veronica like Archie, to the point of fighting over him constantly, but don't mind his fickle heart, is up for multiple interpretations. Some fans think that the two have Unresolved Sexual Tension and may not even know it. Lampshaded in stories where they argue over other subjects, compete furiously over some prize, declare the "ending" of their relationship, and then try to win each other over again. One story even had Archie giving them couples' therapy advice, claiming that it was what his parents did after their own fights.
Jughead has been interpreted as asexual by many, or as being in love with Archie but hiding it. The latter got especially popular when Kevin appeared, and he and Jughead got along easy. However, there was a story arc that addressed this directly; it turns out it is a case of The One That Got Away. As of the reboot, Jughead is canonically asexual.
Is Archie a milquetoast goodie-goodie who borders on being a Canon Sue instead of the everyman he is meant to be? Also, is he just an absent-minded date, or is he so selfish, fickle and manipulative as to be after Anything That Moves?
Every main character, especially Betty. Each character drifts from likable to completely insane. The disparity is due to both Characterization Marches On and Depending on the Writer. Some stories have any given character behaving kindly and friendly, others depict the same character(s) as being cruel, manipulative, obsessive, and/or violent.
Kevin Keller. On one hand, he has many followers who think of him as a surprisingly interesting character for being a positive portayal of an openly gay character. Others think that he is slowly usurping Reggie's place in the Five-Man Band, noticing that he is appearing less and less in favor of Kevin, without having much in the way of a fleshed out characterization.
Best Known for the Fanservice: A few readers know the series only for the beautiful girls drawn by Dan DeCarlo, especially Betty and Veronica. There is a reason why they appear so often in bikini or other skimpy outfits.
Critical Research Failure: In one 1990s strip, Miss Grundy was putting on a play about American heroes or some such theme. She assigned Archie and Jughead the part of Astronauts, and Betty the role of Florence Nightingale.note For those who don't know, Nightingale, the pioneer of modern nursing, was English.
Sabrina the Teenage Witch became so popular as to get her own comic series and several TV shows, most famously a live action sitcom starring Melissa Joan Hart.
A comic had Sabrina switch everyone's gender. Fans really want more of Reggie's Distaff Counterpart, Regina, who is a proper Alpha Bitch. Archina, Billy, and especially J.J. are very popular (a picture of them and Regina can be found here◊)''. Archina has cute Girlish Pigtails and people enjoy her reverse harem more than the usual version, while J.J.'s fashion choices, apathetic personality, and Big Eater qualities make her attractive to people (much more so than normal Jughead).
Fridge Logic: Just why was "Cousin Leroy" always there without any other members of his immediate family, anyways?
If Big Moose is too dumb to tell what 2 + 2 is, or where the Leaning Tower of Pisa is, then how the heck did he make it all the way to being a junior in high school?
He's a star athlete, usually the best one in any sport they compete in. And, Dilton did tutor him well enough to get a 75 on a science test so he [Moose] could stay on the basketball team.
One Very Special Episode tries to establish Moose as a dyslexic, which could at least explain some of his poor schoolwork.
Germans Love David Hasselhoff: The franchise is (or was, at least in the 1980s and 1990s) very popular in Mexico, such that a theater play existed there, not to mention many of the spin-offs are still published in Mexico to this date.
Of course, being such a long runner, this is to be expected. In one comic, done when mobile phones were new, Sabrina (way before her sitcom days) crashes into a telephone pole while talking to one while flying on a broomstick. (Little would anyone realize how dangerous distracted drivers would become.)
One digest featured a series of stories wherein the conditions within the school after Mr. Weatherbee had installed surveillance cameras brought up comparisons to 1984 and was followed up with a series of stories dealing with corrupt bankers, crippling regulatory edicts from the government against private business ownersnote though Mr. Lodge's resolution of that one is a Moment of Awesome for him as he basically told the Pentagon to stick it where the sun don't shine, and stifling the freedom of the press by arresting a journalist [Reggie's father] for printing a negative story. Such incidents have not only happened in real life, but in greater magnitudes since the time of printing.
Ever since Jughead got confirmed as asexual, Trula Twyst's attempts to get him "interested" in girls seem a lot less like a gag and a lot more like Cure Your Aces.
One True Threesome: Over the years as Betty and Veronica have become friendlier and friendlier, shipping both with Archie in a full threesome relationship has become incredibly popular.
Shipping: A common Fan Fic concept features Jughead paired up with someone, usually Betty. Some writers themselves have commented that they would like to see the two put together, but ultimately can't break up the ultimate Love Triangle at the heart of the stories. Also helped by some actually printed stories. In one story, "The Big Surprise", Jughead is the only character who realizes that Betty sacrificed her own chance at happiness, in order to mend a situation that would permanently end Archie and Veronica's relationship. Jughead's reaction is to tell her: "... if I ever start to like girls, you're going to be the first one I go after!"
Ship-to-Ship Combat: It is borderline encouraged. Betty/Archie vs. Ronnie/Archie has been a long-standing debate for decades, even if many people are basing it on second-hand knowledge as they have never read the series. Archie/Jughead, Betty/Jughead, Ethel/Jughead, Betty/Reggie, and Reggie/Veronica are often added into the mix, too. Plus relationships involving Cheryl Blossom, Midge Klump, and various supporting characters, that get their own spotlight at times.
Strawman Has a Point: One of the Love Showdown comics has Cheryl's Jerkass brother Jason taunt Archie by saying, "At least I'm not some freckled-face goofus who can't make up his mind about a woman." That is a perfect description of Archie.
They Wasted a Perfectly Good Character: Big Ethel. As detailed in this blog post, she was a character who was ugly and physically unattractive, yet was also a confident and kind-hearted person who never let her looks get in the way of her pursuit of Jughead. While that would seem like interesting fuel for some stories revolving around her, she actually only made occasional appearances in the comics (the Spire-produced Christian-themed comics that gave her a bigger role don't count), most of which played off her physical appearance for cheap laughs. It doesn't help that A) Jughead was eventually given his own Love Triangle with two new characters, with Ethel being Demoted to Extra for the time being, and B) starting around the 1980's, her appearance began gradually changing from being "the poster child for Gonk" to simply "plain" (which, as pointed out in the previously-linked blog post, ruins the potential "ugly on the outside, beautiful on the inside" message, and instead unintentionally sends the message that the concept of "ugly" characters is completely unacceptable).
Unintentional Period Piece: Some of the stories turn into this as times change. One story had the Coopers' furnace breaking down during a cold snap and the Andrews inviting the Coopers to stay with them until they get the furnace fixed. Betty answers the Andrews' phone when Veronica calls for Archie, and Ronnie thinks that Betty sneaked over to the Andrews' place to be alone with Archie, even though her parents are there too. Veronica goes marching over to confront them, and the story ends with Fred and Hal carrying a frozen Veronica into the house. Nowadays, with more and more people abandoning landlines, Veronica would simply have called Archie on his own phone instead of accidentally talking to Betty.
One big case of values dissonance comes from any depiction of gender roles throughout the years. Sometimes, just the idea of a woman being a doctor or a lawyer is a punchline, or how Jughead used to be called a "woman-hater", which sounds needlessly misogynist—today he would be called asexual (and is, in the reboot).
Ugliness used for comedy doesn't fly as well anymore, so Ms. Grundy, Big Ethel, and Archie himself have been given subtle face lifts over the decades. With Archie it happened quickly, but Ethel in particular looks unrecognizable.
One story called "Overbooked" has it that Riverdale High requires mandatory hours of community service from all students. Mr. Weatherbee forces Veronica to serve as a replacement librarian at the city library, since one of the regular librarians is on sick leave. In part, he hopes to stop her from flirting with all the high-school boys. At the library, Veronica receives unwanted romantic advances from prepubescent boys, nerdy young men, and dirty old men (some of which are more than 70 years older than her and are touching her without permission). Veronica exits the library while being pursued and sexually harassed by a small army of boys and men. Weatherbee blames her for supposedly flirting with everyone. The supposed comedy of the story involves her obvious discomfort at being treated like that, and at Weatherbee blaming the victim. It has not exactly aged well as a concept.
An old story, set in the summer, has Hiram Lodge noticing Betty and Veronica window shopping while wearing short pants. He scolds them for wearing shorts in public, and punishes them both by having them clean the pool. Later in the story, Hiram leaves on an errand with his car, while wearing the short pants he uses to relax within his home. When the car breaks down, he has to walk in these shorts. Entire crowds laugh at his supposed humiliation, and he is very embarrassed by the time he returns home. How many people would currently be bothered with men or women wearing short pants around town? There is not much shock value in them.
Very early stories had minor African-American characters either portrayed in Blackface, or characters actively participated in wearing Blackface themselves, such as when Riverdale High put on a production of Uncle Tom's Cabin.
And how! In fact, the original name suggested for this trope was Emo Jughead. Despite the fact that Jughead is usually the most offbeat and non-conformist of the group, he was always the one shown experimenting with new fads or subcultures of fashion. He has been an Emo Teen, a Goth, a skateboarder, a punk, etc. over the years, generally hopping on as a sign of his own counter-culture compared to the more milquetoast cast.
Sometimes digests include old stories reprinted with modern cultural references such as American Idol now awkwardly inserted through editing. The obvious change in lettering doesn't help.
And, at other times, they don't bother to correct the art. One story printed at least twice has Archie's grandparents showing vacation movies first recorded to video tape and, in the second run, burned on DVD, but the art in both versions clearly shows them handing a VHS tape to Archie to queue up.