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.
Audience-Alienating Premise: Critics who complain about the dolls, books, and movies often bring this up after their first complaint. "I just don't get it. How could a doll line aimed at eight-to-twelve-year-old girls, just when they're being pressured to give up dolls and grow up faster, setting out to teach them about the Civil War or the Great Depression, and sitting at a high price point... be popular?"
Awesome Art: The Historical Characters' book illustrations are not only very pretty to look at, but they reflect the time period and setting. For example, the family portraits in Molly's books are in black and white.
The portraits in Kirsten's series are the only ones to have full-body images of the families, and have full background images as well.
Awesome Music: The accompanying background music for the online game "Kirsten's Winter Stars" is absolutely gorgeous. See for yourself: 
The soundtrack to Felicity's movie has some lovely fiddle and whistle tunes as well.
Crack Is Cheaper: Look outside the fandom (or even inside it, though fans will praise the quality and significance for what you pay) and you'll find that this is the number one complaint leveraged against the franchise.
Even Better Sequel: Samantha: An American Girl Holiday was, by all accounts, thoroughly good. But its successor, Felicity: An American Girl Adventure, well surpassed it in quality thanks to a universally talented cast, with Marcia Gay Harden and a young Shailene Woodley in particular standing out for their luminous performances.
Fan Nickname: "Blondiebeth" for Elizabeth post-Adaptation Dye-Job, "Princess Samantha" for Samantha (and the scaled-up "Pretty Princess 'Mantha", usually by detractors of her popularity), "Valerie the Inept" for author Valerie Tripp by fans of the authors who preferred to tackle more serious issues or whom they perceive as producing better-quality books.
One of the illustrations for Happy Birthday, Addy! features a wooden ice cream maker/mixer labeled "Ice King".
Ho Yay: A lot of people see some or all of the Best Friends relationships as Romantic Two Girl Friendships or a precursor to more. Then there are the main characters with the My Journey girls... especially Samantha and Ruby, who in one story path switch clothes and in another sneak out to go swimming in their underwear.
Memetic Mutation: At least some of the characters from the series ended up in a number of Hitler Rants parodies on YouTube. Some of the characters who appeared in the parodies, namely Felicity and Kit, were depicted as way off-character, either ending up being a Screwy Squirrel in the vein of Fegelein, as in the case of Felicity, or ranting like a maniac like Kit and Samantha.
"Kirsten gets eaten by a bear!" (She doesn't, but she does encounter one in her summer book.)
Misaimed Fandom: American Girls Premiere, a computer game released in the late '90s that gave players the ability to write and perform plays about the various historical protagonists and their families and friends. It was supposed to be educational, but it was hard to take the game seriously between the creepy robot voices and the strange movements (characters could even float or walk through walls, and even normal gestures were always exaggerated). As a result, way more people used the game for parodies, Downfallspoofs and poop jokes than for its intended purpose, helped along by the game's almost total lack of a word blacklist.
Narm: Jiggy Nye beating Penny in the Felicity movie.
In the first Addy book, the slave driver makes her eat slugs off the tobacco plants.
In Samantha's movie, a boy working in a factory gets his finger caught in a machine.
The American Girl magazine runs a story contest every year. One year, the winning story was about someone who befriends a mysterious girl down by the lake. At the end, the mysterious girl turns out to be a malevolent ghost. The ghost drowns the main character, who then takes the ghost's place, waiting for the next victim to wander by.
Periphery Demographic: American Girl actually has a lot of fans who are adult women, often doll collectors. They can often be the strictest fans, especially those young women who got into the dolls as kids and apply the Nostalgia Filter.
Ruined FOREVER: People who haven't touched the series in decades and even long-dedicated fans whine that the series is ruined FOREVER because a) characters get archived, b) new stories and items come out, and c) the Girls of the Year exist (or that modern dolls exist at all). It even makes it to news articles likethese.
The Scrappy: Kailey. The hate she gets is so bad that it spreads over to any character whose story has an environmentalist message, like Julie or Lanie.
Replacement Scrappy: Agnes and Agatha, who shifted Nellie to the side to be "safe" friends for Samantha who weren't walking metaphors for classism and the bad parts of the Edwardian era.
They Changed It, Now It Sucks: Whoo boy. Mattel took over from Pleasant Company in 1998, and remodeled the dolls and outfits as well as retiring a lot of items. In some corners of fandom, anything made after 1998 is utter crap.
The revamp of the Historical Line with BeForever has led to this opinion in some places.
Unfortunate Implications: It's happened a few times, such as the famous incident where Marisol was criticized for moving out of the inner city because it was unsafe and therefore making her old neighbourhood (a real place) look bad. Newsmagazines in 2009 tried to play this up and create a controversy out of minor character Gwen, labelling her "the homeless doll", even though she gets a place to move into partway through the first book she's in, we don't even know she was homeless until The Reveal near the end of said book, and she's not even the main character (that'd be Chrissa).
Addy being Demoted to Extra. She and her items rarely appear in the catalogs, usually with just a picture of her and a note to "find her things at American Girl. com!" Then there are the fans who complain about her hair, her skin tone, her accessories, etc.
Consciously averted with many of the minority characters, who fly in the face of ethnic stereotypes. Addy is very intelligent, Cecile is rich and popular, Rebecca is generous, Josefina is shy, and none of them could be considered lazy. Unfortunately played straight with Lindsey, though...
The Woobie: Nellie O'Malley has a very poor home life compared with Samantha, who also happens to be an orphan.
Emily, especially in Molly's movie. Not only has she witnessed firsthand the terrible effects the war has done to her life in England (bombed out houses, taking refuge in the subway tunnels from the blitzkrieg, the death of her mother), she even has a nightmare about being attacked.