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.
Adaptation Displacement: While the TV specials are generally better known than the comic strips, there are a rather vocal section of fans who take their cues from Schulz as far as treating only the strips as canon and ignoring pretty much anything from cartoons, even if it's minor stuff like the Super Bowl special giving Marcie a last name (which was never stated in the strips).
Alternative Character Interpretation: A lot, but specifically that Peppermint Patty and Marcie are Schoolgirl Lesbians. In-strip, though, both are clearly crushing on Charlie Brown. A bit further out, there are those who consider Peppermint Patty to be omnisexual/into bestiality, due to her firm belief that Snoopy is 'a funny-looking kid with a big nose'. She got enlightened later, but still treats him the same way.
Similarly, there are some who consider Lucy's cruelty toward Charlie Brown as a mask for her own romantic feelings for him...yes, there are people who act like that.
There are also those who think Schroeder is simply Asexual and aromantic.
In the foreword to the 1975-76 collection, Robert Smigel (an SNL writer and the guy behind Triumph The Insult Comic Dog) argues against the popular view of Charlie Brown as a Determinator - see that entry below.
Charlie Brown didn't keep trying to kick Lucy's football out of some inner strength and Horatio Alger resolve we were supposed to admire. He did it because he was weak. He was flawed, and he couldn't help himself. But that's exactly why we love him.
The reason Violet constantly says My Dad Can Beat Up Your Dad is because she doesn't want anyone to know that she wishes he'd spend more time with her.
The first time we hear it (main time), Snoopy, as "Flashbeagle," goes into a 1980s dance club and shows he has dance moves (and dressed in a "Flashdance" outfit—headband, torn sweats, leg warmers) to the humans there.
The second time we hear it (reprise), a student heckling Sally and Snoopy pulls out a boom box and turns it on. Snoopy hears the rhythm and music, causing him to dance all over again. He becomes Flashbeagle without the outfit while the other students dance. This gives Sally her first "A" in Show and Tell and lets her defend Snoopy's behavior to Charlie Brown.
Creator's Pet: Rerun, who pretty much usurped control over the strip in the last five-six years at the expense of every character not named Lucy, Charlie Brown, and Snoopy. Spike, Snoopy's older brother, also fits the bill as well.
Dork Age: There are lots of opinions on when the strip's Golden Age was, how far it fell from that over the years, and exactly when the Seasonal Rot first set in, but pretty much everyone agrees that the 1980s were the weakest period, with frequent rehashing of old ideas, misguided attempts at relevance, and the inexplicable rise of Snoopy's brother Spike. Some of this was due to circumstances beyond Schulz's control, namely a heart attack that forced him to slow down his working pace.
Ear Worm: "Linus and Lucy". How much so? One poll reported that the theme was the most recognizable piece of music in the world.
Ensemble Darkhorse: Snoopy. The first couple of years of the strip had him being a non-entity who never spoke and was treated as a secondary character. But he quickly became arguably the most famous character of the series.
Alternatively, you have Lucy (upstaging female lead characters Patty and Violet) and Peppermint Patty, who had her own supporting cast of sorts (Franklin, Marcie and occasionally Josť Peterson).
Schulz himself noted the discrepancy between Pig-Pen's popularity and his rare appearances in the strip
Peggy Jean is surprisingly popular in fanfiction - maybe because she's the only girl that treats Charlie Brown with nothing but kindness.
Fanon: Several elements of the strip, including the Little Red-Haired Girl's actual name and Marcie's last name You're in the Super Bowl called her Marcie Johnson, but Schulz has said that he never considered the animated specials canon. Another special gave the Little Red-Haired Girl's name as "Heather." Again, not canon, but fanfiction uses it anyway, usually on the grounds that they have to call her something.
Fanon Discontinuity: Fans of the newspaper strip versus fans of the animated cartoons, as far as whether or not character details that are expanded upon in the latter (such as Marcie's last name, the number and names of Snoopy's siblings, and what the Little Red-Headed Girl looks like) should count as canon.
Follow the Leader: Peanuts was influential on comic strips in general, but a few strips took very specific inspiration from it:
The Perishers (1959-2006) was a British strip about a group of kids and a dog. The humor was more British-style and the artwork was more in line with British strips like Andy Capp.
Winthrop (1967-1993). After Peanuts became a cultural phenomenon, Dick Cavalli Retooled his strip Morty Meekle to be about...a group of kids and a dog. It also had some slightly altered Expies of Peanuts characters: instead of Pig-Pen, an obsessively clean boy (Spotless McPartland); instead of Lucy, a belligerent boy, and so on. The artwork was reminiscent of early Peanuts as well, but it did feature some adults in the cast.
"Funny Aneurysm" Moment: The very last strip, like all comic strips, was written many weeks in advance...and was printed the day after Charles Schulz died.
Germans Love David Hasselhoff: At least two translations of the strip (the French one and the Swedish one) were renamed after Snoopy. He's also very popular in Japan.
It would be interesting to note that, if you look at Yoshi from the Super Mario series' look and personality, it's very similar to Snoopy. Even similar enough to think Yoshi might be an Affectionate Parody in tribute to Snoopy.
A peculiar example (almost a form of Covered Up) is that in the USA the animated specials are better known than the original strips, whereas in other countries it's usually the other way around.
I Am Not Shazam: When the strip first came out, people naturally assumed that Charlie Brown's name was "Peanuts". This frustrated Charles Schulz, who had predicted that this would happen.
Iconic Character, Forgotten Title: Many people thought the comic strip was called "Charlie Brown" or "Snoopy". Sunday comics added subtitles such as "Featuring Snoopy" or "Featuring Good Ol' Charlie Brown". The reason for this, as mentioned in I Am Not Shazam, is because Schulz didn't want the strip to be named "Peanuts" and didn't want any readers thinking Peanuts was Charlie Brown's real name.
Lucy pulling the football away from Charlie Brown has become a popular analogy. Political pundits especially seem to love it.
Moral Event Horizon: Lucy crossed it in "It's Your First Kiss, Charlie Brown", when she decides to humiliate poor Chuck as opposed to give him a Throw the Dog a Bone moment by letting him kick the ball. Further cemented in that at the homecoming party, she decides to blame Charlie Brown for losing the game, even though it was her fault Peppermint Patty's team lost the homecoming game.
Narm Charm: The animated specials, particularly the very early ones, have a great deal of this.
Nausea Fuel: An early 1970s Sunday strip has this, when Lucy drinks some soda with a straw that Snoopy used without her knowledge. The disgusted expressions that Charlie Brown makes because of this distract Lucy from their conversation.
While not as soul-crushing as Snoopy Come Home, A Boy Named Charlie Brown has a pretty melancholic feel to the whole thing. The basic plot is Charlie Brown dealing with the unrelenting misery and failure that is his life, getting a Hope Spot when he gets a chance at a regional spelling bee, and returning in disgrace after he loses.
Toy Ship: Many of the strip's male/female relationships would qualify as this.
Values Resonance: A Charlie Brown Christmas' denouncement of commercialism (which carries over into A Charlie Brown Thanksgiving and It's the Easter Beagle, Charlie Brown as well) and presentation of the True Meaning of Christmas.
Which makes later handling of the show even more ironic; due to the fact that networks generally push in more and more commercials into episodes, for several years the special aired heavily truncated. Fan backlash ultimately made them back away from it, giving the special a full hour and tossing in a short from a Christmas anthology special to pad things out so they can air it uncut.
There's also a bunch of still-relevant political humor in You're (Not) Elected, Charlie Brown and the strips on which it was based. The fact that they haven't dated is probably due to Schulz lampooning the overall election process rather than a current election or event of his day.
Viewer Gender Confusion: Some people actually thought that Peppermint Patty was not a tomboy, but a real boy. It doesn't help that in some of the animated adaptations, she is voiced by a boy, and that in the 1980s and '90s, it became a little more acceptable for young males to have longer hair than it would be in the 1950s-1970s. (Where it was older men who had longer hair primarily!)
Plus, she's drawn with shorts - Schulz would often draw the other girls with skirts.
This was just made worse in the strips constituting "She's a Good Skate, Charlie Brown", where Peppermint Patty goes to get her hair cut by CB's father, a barber, then comes running out, her hair all but scalped, screaming at him, "You didn't tell him I'm a GIRL!"
What an Idiot: An entire arc was dedicated to Peppermint Patty attending a "cheap private school" Snoopy recommended and not realizing it was an obedience school until after she graduated and the principal told her when she showed him her diploma as proof that she doesn't need to go back to school.
She then blamed Snoopy, and looked for him in order to beat him up, but forgave him when he saved her from the cat who lived next door to Charlie Brown (which she had mistaken for Snoopy in a cat suit).
Let's not forget that Patty for the longest time thought Snoopy was a "funny-looking kid with a big nose." It was not until a series of strips in 1974, when Patty announced she was quitting school and moving into "Chuck's guest cottage," that an irate Marcie finally pointed out the truth to her.
And a series of strips from 1982 or so when Patty decided to transfer to a school for gifted children because she thought it meant they would give her presents.
Charlie Brown, whenever his optimism is crushed for the umpteenth time.
Linus, whenever the Great Pumpkin fails to appear.
Peppermint Patty gets her moment when she sees the Little Red Haired Girl and how pretty she is, and realizes why Charlie Brown always loved her. It's enough to drive her to tears, and anyone who's ever had an unrequited crush probably knew exactly how she felt. Thank God Linus was there to listen and cheer her up.