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.
Angst Aversion: This movie is notorious for being very depressing to watch. It has everything from a brutal dictatorship to child abuse, to the inevitable prospect of a slow and sad death. The list goes on.
Complete Monster: Lots-O-Huggin' Bear. He allows the toys to be broken by the too-young toddlers in the Caterpillar room, and will do anything just to keep his reign. Here's just a short list of his atrocities: lying to Big Baby and Chuckles that their owner had replaced them just so he wouldn't be alone in being lost, ordering the resetting of Buzz Lightyear, watching him beat down his former friends with a cold sense of satisfaction, beating Chatter Telephone to a pulp in order to find out about Woody's escape plan, and, in the climax of the film, he leaves Andy's toys to burn in the Incineratorafter they risked their lives to save him, and he does so with a sadistic smile, a mocking salute and while yelling out "Where's your kid now, sheriff?". And while he does have a tragic backstory, there's a scene where Woody point blank calls him out on how weak it is (his owner replacing him with a new Lotso was, considering she doesn't know toys are alive, a sign of how she loved Lotso; Woody says that it was Lotso who abandoned her). What makes it worse is there was almost no warning that Lotso was going to be the villain going into the movie. Sid and Stinky Pete to a degree had a glimpse of their villainy in previews but Lotso was promoted as a grandfatherly figure in trailers and commercials. And finally, he is the only villain in the franchise that never sought redemption. In fact, he only faked gratitude when Woody saved him, and ultimately he has gone down in the Pixar history as the most vicious villain that the company has created.
Continuity Lockout: True, this isn't The Matrix Revolutions but viewers new to the series may wonder why the green aliens are constantly talking about "the Claw". An attempt to bridge this gap is made when they first arrive at the daycare. The aliens point at a construction vehicle toy with a claw and say "The Claw!" to establish that connection with new viewers.
Crosses the Line Twice: The scene where the daycare children rough up your toys is a little dark, but then Jessie's head gets dunked in paint. The line is crossed again when Rexloses his tail. Then again when Buzz is used as a mallet.
One working theory is that the 3rd movie is a metaphor for the afterlife. See this essay for more info.
Lotso never made it out of the dump.
Genius Bonus: Potato Head using a Tortilla and a Cucumber while his body was trapped. Unless you're a vintage toy collector, you might not know that was how Mr. Potato Heads were actually sold: They were originally only a collection of parts meant to be used with real vegetables, and were later sold with plastic bodies to discourage food wastage.
Harsher in Hindsight: When Woody lists the friends they lost while Andy grew up, he mentions Wheezy. In Toy Story 2, Woody saved Wheezy from being put in a yard sale.
Like You Would Really Do It: Averted. The incinerator scene was so intense that a lot of fans watching for the first time were genuinely afraid Pixar actually was going to have the nerve to destroy their iconic, beloved characters. Even some Genre Savvy viewers who noticed that the Little Green Men had been conveniently removed for the moment have admitted that they wound up forgetting this when the scene actually came up.
Magnum Opus: Often considered one of Pixar's absolute best, along with Up from the previous year. Fittingly, both were nominated for the Academy Award for Best Picture.
Moral Event Horizon: In Toy Story 3, Lotso had already established himself as a dog-kicking machine as he tortures and corrupts the toys during the movie, but irrevocably crosses the horizon when he pretends to try to turn off the Conveyor Belt of Doom leading to the incinerator, then leaves the other toys to their deaths with the remark "where's your kid now, sheriff?", complete with a mocking salute and evil smile. This after he pretended to be redeemed and after Woody and Buzz had just risked their lives to save him. So much for Rousseau being right this time, as is usually the case for Pixar.
What Do You Mean, It's for Kids?: Much of the humor is over young heads, and a lot of kids get frightened and often even leaving during the Monkey Scene (A few theorized the 11-year Sequel Gap helped Pixar aim for a Darker and Edgier route). Even worse is that it once played on the Disney Junior block and had a tie-in with Pull-Ups training pants.
Most of the main cast fall under this; they've lost many of their friends, they're not played with any more and they're doomed to life in the attic, which isn't so bad but can never compare to Andy's childhood. Then they get thrown out by accident.