Applicability: Two innocent young kids become friends because they're oblivious to how the rest of the world sees them, and then grow up into the roles society expects of them and are torn apart.
Broken Base: Disney fans are split between whether this is a heart-wrenching childhood classic or the red flag of Disney's Dork Age finally hitting an all-time low.
The Dinky and Boomer sidestory is either considered Padding or the best part of the movie.
Family-Unfriendly Aesop: It basically says The Power of Friendship and The Power of Love can't overcome hard-wired reality. Also that racial differences cannot be overcome and that everyone's just better off ending their friendships and living apart from one another with their own kind. Nice going, Disney; this is one of the rare instances where they DIDN'T attempt to use either classic trope to get a fully happy ending.
Just Here for Godzilla: Some really like the film solely for the scenes with the birds trying to catch the caterpillar.
Moral Event Horizon: Amos Slade comes dangerously close to crossing it when he attempts to shoot Tod after he saved their lives, but manages to avoid it when Copper convinces him that he's not their enemy.
Narm: Silly, empty-headed woman! Complete with a make up song.
One-Scene Wonder: The bear is onscreen for less than three minutes, but no one who's seen it will forget it any time soon.
Padding: The Dinkey and Boomer side-story where they spend their time trying to catch a caterpillar serves no purpose but to add a couple comical scenes for the movie, but to some people, it's the best part.
Shipping: Given the fact that their relationship drives the plot, it's not surprising that Tod and Copper get their share of this. Even better, it takes the above mentioned Applicability to a whole new level...
Tastes Like Diabetes: A common misconception of the film due to how it's advertised. While there are a few overly cute scenes during the eponymous duo's childhood, the movie is actually taken very seriously and is much more adult-appealing than most people seem to realize.
They Wasted a Perfectly Good Plot: Some people think Chief should have been Killed Off for Real to make Copper's anger more justified and overall have made the latter half of the movie a lot darker. Apparently, Disney was going to, but decided against it because they thought it'd be too dark. Chief's original fate is apparent when Copper finds him after he's jumped off the bridge; a dog lying motionless with his nose in the water is pretty much dead. But Disney decided to draw the line there.
The Woobie: Tod can be this. His mother is killed when he's only a baby, he gets chased and shot at by Chief and Slade, respectively (twice!), his best friend disowns him and wants him dead, his owner drops him off in a wildlife preserve for his own safety leaving him without survival skills and a friend in the world, and on top of it all, his neighbor (the badger) is a complete Jerk Ass to him. Things get a lot better after he meets Vixey, though...then worse...then better.
The widow as well - it's made very clear that Tod is her only source of companionship, and that it's just as heartbreaking for her as it is for him, if not more so, when she has to Shoo the Dog to protect him.