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.
There are a few people disappointed at the lack of characters from Disney's renaissance era, with most of the playable characters coming from most of Disney's post-2000 work, like Wreck-It Ralph and Pirates of the Caribbean.
Some are disappointed at there are hardly any characters from the Disney Animated Canon at all. The few that are are only from post-2010 CG films. There wouldn't be any 2D animated characters until Stitch, Aladdin and Jasmine were introduced in 2.0.
Many Pixar detractors and "classic" Disney fans were upset that the first game's roster was roughly half Pixar characters and half "actual" Disney characters. The fact that more than half of the game's playsets were based on Pixar movies while fan-favorites like Jack Skellington and even Mickey Mouse were toybox exclusives didn't help.
Cars characters being in the games. They're, well, cars so they really stand out.
Phineas and Perry are in despite being from animated series rather than movies. Ideally this could make way for even more potential characters and playsets, such as an often requested Kim Possible figure, or a Recess playset. However, some fans are under the impression that it's a one time deal due to their popularity.
The Marvel universe being the main focus of the second game broke the base even further.
There's a further split with people upset that the X-Men & Fantastic Four aren't included, seemingly because of Disney's dispute with Fox over the movie rights to characters. The potential of having the Richards family encountering the Parr family is certainly enticing...
While Big Hero 6 fans are looking forward to play Hiro and Baymax, Hiro has become a fan-favorite for being such a powerful character.
First Installment Wins: Averted. The majority of the roster is comprised of characters from source material originating from the 2000s. The exceptions are Mickey Mouse (of course), Jack Skellington and Maleficent, and that's not counting the Marvel heroes: the oldest character amongst the latter group is Captain America, who made his debut in 1941. This makes him the second oldest character in the entire game behind Mickey. In a notable exception, the game uses Sam Alexander, the secondNova, rather than Richard Rider, the original Nova. It also features Carol Danvers in her Captain Marvel persona rather than as Ms. Marvel.
It's long since been patched, but the PS3 version had a save corruption bug for a while.
The Wii version doesn't have the online functions the HD consoles do. That means you can't upload or download levels created in the Toy Box by other users. There have also been reports of lack of multiplayer in the Play Sets.
The Wii U version of 2.0 added online functionality, but still has frequent framerate drops.
The iOS version of the toybox has lots of problems, such as severe frame rate issues and impractical touch-controls.
Scrappy Mechanic: Leveling up a character after it grows past level five is difficult enough, but try doing it with a toy box exclusive character, and THEN try it after you've completed all the feats!
2.0 makes things quite a bit easier with the addition of "Survival Challenges", which involve an endless series of Randomly Generated "Kill all the Enemies" and Tower Defense levels, giving you plenty of mooks for you to beat up for XP.
Stop Helping Me!: The announcer can REALLY grate on one's nerves after the Umpteenth time he walks you through the "Packs and Tools" and "Mission Log" tutorials. He'll even talk over character dialogue.
They Wasted a Perfectly Good Plot: All of Disney in one video game? That's awesome! We could have Jack Skellington teaching scaring in Monsters U, or Elsa can freeze the ocean in the pirates playset! The possibilities truly are infinite... Oh, they're all designated to their own playset? And some of them can only be used in the toybox? Well, I guess that can be fun, too.