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.
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 could stay on the basketball team.
One Very Special Episode tries to establish him as a dyslectic, which could at least explain some of his poor schoolwork.
Harsher in Hindsight: 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.)
Hilarious in Hindsight: There's some of this too, naturally. An example is Dilton saying that it would be years before anyone gets to the moon.
Ho Yay: Frequently with Archie, as Jughead's famously not interested in girls. Him dating a future descendant of Arch's doesn't help matters.
With Jughead the woman-avoider, though this is usually more on Jughead's side.
Betty and Veronica also have quite a bit of Les Yay between them as well.
Recycled Script: Used often and unabashedly, due to the incredible number of stories already in existence and the short timeframe of an Archie Comics reader. And, of course, no one would notice because they were for kids. Anyone who's been reading for more than a decade could easily pick up a Digest collection and find only the cover story was new to them.
One digest twice featured short strips with Jughead walking into a haberdashery and asking the man behind the counter to take a tie out of the window because he couldn't stand the sight of it/it was so ugly it gave him a headache every time he walked past the store.
The same Jughead gag showed up in two different digests released in the same week of that month.
It's been worse. One digest reused a near-exact version of a joke in two comics on the same page.
This was (possibly) lampshaded on one of the covers. Archie mentions that the comics will now be printed on recycled paper. Either Jughead or Reggie responds, "Your jokes have been recycled for years!"
Both, actually. They did the same gag twice.
A big, current example: several of the "New Look" stories have just been taken (characters, whole sections of dialogue, etc.) from the "Archie Novels" series from the early 1990s. Moose & Midge's break-up, Ron & Betty fighting about Nick St. Claire, and Archie moving away were all topics taken.
There's also the faithful Archie Joke Generating-Laugh Unit 3000, always good for an oldie but goodie, and noted courtesy http://joshreads.com/
Joked about in an episode of Friends where Chandler sells a story to the company where Archie temporarily becomes Reggie's butler to earn some extra money, based on his own time working as Joey's assistant. Joey fails to see the parallel but does wind up remembering that they've done a similar story in the past.
Shipping: A common Fan Fic concept features Jughead paired up with someone, usually Betty. Some writers themselves have commented that they'd like to see the two put together, but ultimately can't break up the ultimate Love Triangle at the heart of the stories.
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's a perfect description of him.
Unfortunate Implications: Super Dickery (the website) shows a cover in which Archie motions toward the bar and says, "We serve anyone!" (in response to Mr. Weatherbee whether he serves crabs). The awkward part? He appears to be pointing at Chuck, his black friend... Come again?
Values Dissonance: One old strip had Archie's dad flip out over Archie asking for ten whole dollars for gas.
On the other hand, considering how notoriously cheap Archie's dad is, this joke might be even funnier now.
The much bigger values dissonance comes from any depiction of gender roles throughout the years. Mild stuff like what it means when a guy in the '50s gives a girl his class pin / class ring (that he wants to go steady with her), to more heinous things like how just the idea of a woman being a doctor or a lawyer is a punchline.
We're Still Relevant, Dammit: And how! (the trope was originally YKTTW'd as Emo Jughead. Despite the fact that Jughead is usually the most unique and non-conformist of the group, he was always the one shown experimenting with new fads or subcultures of fashion. He's 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 awkwardly inserted through text. The obvious change in lettering doesn't help.