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.
Fair for Its Day: Kipling is widely recognized as a jingoist, proud of British Imperialism and all its accomplishments. Certainly there's an uncomfortableness in some of the themes in the books. However, the Jungle Books held some lessons that are still very apposite, and his depiction of the seals' plight in 'The White Seal' is a heartbreaker very much in tune with modern views.
Iron Woobie: Mowgli himself, all the way. His entire life is one long, hard lesson about 1; learning how to be stronger than those who try to kill you, and 2; anyone might betray you and try to kill you before you even understand why.
Jerkass Woobie: Shere Khan, actually. Hunting humans is a crime, but with his injured back leg, he doesn't have much of a choice if he wants to stay alive.
Unfortunate Implications: Killing defenseless babies (cobras still in their eggs) is acceptable if the babies' parents (Nag and Nagaina) were evil.
In the books, he's born crippled, meaning he finds it easier to hunt humans. This is a common explanation for many man-eating predators. The film removes his lameness, and therefore his reason for attacking humans.
Angst? What Angst?: Mowgli seems far more choked up about leaving Baloo (who he's known for all of a couple of days) than his wolf family that raised him for about a decade. In the sequel despite pining for the jungle for so long he does not even make so much as a passing mention of them.
Baloo's concern that the Man Village "will make a man out of [Mowgli]" becomes funnier once you've seen the film's spinoff series TaleSpin, which stars a fully-anthropomorphized Baloo.
Shere Khan is a tiger with a British voice and is implied to be somewhat insane. Richard Waugh later mentions that he used Shere Khan's voice as the inspiration for how he would voice Albert Wesker from the Resident Evil series, who is a really bad individual and also happens to possess feline eyes after a certain incident involving a serum.
Toy Ship: Mowgli can't be older than ten, but that doesn't stop the similar-aged village girl Shanti from making goo-goo eyes at him.
Unfortunate Implications: To some, an orangutan (an ape of sorts) singing about wanting to be human might somehow come off as racist. It doesn't help that while Louis Prima is Caucasian, they had intended for Louis ARMSTRONG, an African American to voice him originally.
Villain Decay: Sure, Kaa gets a bad rep around here for his horrendously decayed personality and role in the story, but he was legitimately threatening in the original movie. In The Jungle Book 2? Not so much.
Ear Worm: From Rikki-Tikki-Tavi. "Who has delivered us, who? Tell me his nest and his name!"
Fridge Brilliance: In "Mowgli's Brothers", Shere Khan is portrayed as a white tiger rather than the normal orange tiger from the original book and all other adaptations, despite the fact white tigers have existed only in captivity since 1951, and would have difficulty surviving due to the lack of camoflague as well as health problems. However in the book Khan has a crippled leg, which rarely appears in adaptations, such as this in which all of his legs are normal, meaning that being a white tiger replaces his crippled leg as his disability. The story also takes place before 1951, making it more possible.
For the 2015 Jon Favreau adaptation:
Base Breaker: The announcement that Scarlett Johannson would be voicing Kaa. Some think it's a clever new take on the character, whilst others think that it is changing the character too much.
The film itself. Is it another Disney Live-Action Adaptation, that's going to try to make things Darker and Edgier, like Maleficent and The Lone Ranger or is it a chance to make up for the appalling 1994 live action movie?
Win Back the Crowd: After the disappointments that were Maleficent and The Lone Ranger, an aim of production was to do this. Basically, the aim was to use everything that made Alice in Wonderland good that other productions had missed. For example:
Accuracy to the source material (i.e. no forced romantic interests, accuracy to the characters, but at the same time making them new and interesting).
The announcement that the animals would actually talk in this version, unlike other live action versions.
And that, for one of the first times in adaptation history, Mowgli would be played by a non-Caucasian (well, mixed-race, but still...)