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.
The 'Arkenstone Debacle' while commonly read as being an example of riches induced covetousness on the part of Thorin, is written in such a way that no party comes out completely clean or wholly villainous- Thorin, while stubborn, is ultimately just safeguarding the treasure for his long-suffering people and (quite reasonably) refusing to negotiate a share for the men of laketown under threat of violence. Thranduil, for all his talk of tarrying long ere he begin a war for gold has nevertheless parked an army outside the gates of people who he had locked up a mere couple of weeks before, and Bard, while possessing the most honourable motives of the main factions, and probably the best claim to a portion of the treasure, has not only allied himself with the explicit enemies of the person he's bargaining with but seems perfectly willing to launch a surprise pre-emptive strike on Thorin's much needed reinforcements led by his cousin!
Bilbo himself also doesn't come off well in that scene on some interpretations. He knows (and admits as much to himself) even when seizing the Arkenstone that although Thorin said he could choose his own share of the treasure as a reward for his efforts, it probably wasn't going to include that. Yet he still keeps it and gives it to the besieging army, with at least some idea of what is likely to happen as a result.
This is explicitly to force Thorin into letting him pay them off from his own share.
Actually Bilbo nicks the Arkenstone before any of that comes up- kind of concurrently with Smaug attacking Laketown and before Bard ever arrives to make a claim on the treasure. Although Bilbo does the 'right' thing (even if it does go tits-up) in the end, he steals the Arkenstone purely for his own keeping originally.
Thorin Oakenshield: stalwart, honorable leader of a mighty company of Dwarves, out to reclaim his ancestral homeland? Or an avaricious, stubborn fool in way over his head, who leads an inexperienced, underequipped group of bumbling idiots on a suicide mission for the sake of honor?
Gandalf: Many readers assume Gandalf's involvement with the quest is down to his noble character and sympathy for the Dwarves, but can be alternatively seen as a pre-emptive strike, essentially manipulating the characters into forming a hit-squad to keep Smaug from joining the Necromancer's army.
Anvilicious: When the golden cup is stolen by Bilbo, Tolkien comments that Smaug's rage is the sort "that is only seen when rich folk that have more than they can enjoy suddenly lose something that they have long had but have never before used or wanted". Considering that it's a comparison to something that just happened, it's quite redundant, and only seems to be there to prove a point. But it's agood point.
From the book, when Bilbo tries to pickpocket a troll, the money purse suddenly says: "Ere, 'oo are you?", leading to him getting caught. It's never explained how the bag can talk, and it never does so again, nor does it get any comment from any of the charactes. And the narrator just states that "Trolls' purses are the mischief". In the movie this was thankfully removed, instead the troll confuses Bilbo with a piece of cloth. However in contrast to The Lord of the Rings movies, seeing trolls talk and being somewhat intelligent might count as BLAM.
Also from the book: the stone giants throwing rocks at each other while the party is trying to cross the Misty Mountains. They're never mentioned again in the whole book (except for Gandalf making a passing comment that he'll have to get a "friendly giant" to block up a pass so that goblins can't get through) and given only a passing mention as rumor near the beginning of Fellowship of the Ring.
The scene is kept in the film with Bofur exclaiming "Stone Giants! The legends were true!" to let the viewers have some idea of what the hell is going on. The movie giants are literally made of stone, and don't seem capable of speech. Granted, it's a little better in the film because the Company ends up being chased into the cave that leads to Goblin Town while running from the giants.
The first edition of The Hobbit, before Tolkien got the idea of integrating it into his wider legendarium, mentions lamp-posts and policemen. These were removed in subsequent editions.
Ensemble Darkhorse: Given how well-known of a character he's become, it can be hard to forget that Smaug isn't actually in that much of the story, comparatively speaking. But he's easily the most memorable part of it.
Gandalf's name is taken almost wholesale from a character in the Voluspa known as Gandalfr, a Dwarf who wields a staff and is king of the elves. Other aspects of his personality are taken from The Kalevala.
Unfortunate Implications: After The Lord of the Rings was published, Tolkien once said he partly modeled his Dwarves on the Jews, based on both peoples being exiles from their original homelands. Dwarvish was also modeled after Semitic languages, and the Dwarves continued to preserve their own language and culture while living among different cultures, much like how Jews have done. However, stretching his words and applying them retroactively to The Hobbit, written over 30 years prior, leads to some questionable passages:
''There it is: dwarves are not heroes, but calculating folk with a great idea of the value of money; some are trickery and treacherous and pretty bad lots; some are not, but are decent enough people like Thorin and Company, if you don't expect too much."
Characterization Marches On in The Lord of the Rings, since Gimli and the dwarves are clearly heroic despite their prejudices, which Gimli in particular overcomes. The dwarves of The Silmarillion are also portrayed as much more serious and overtly heroic than the often bumbling ones of The Hobbit, which they predate. A possible bit of Fridge Brilliance in that Thorin and company actually recaptured the homeland the dwarves were exiled from.
Also a superbly worded response to a Nazi sympathetic publisher's letter asking if Tolkien was of "arisch" descent makes it highly unlikely that Tolkien intended any offense (although it is still possible that he subconsciously absorbed anti-Semitic stereotypes):
''"I regret that I am not clear as to what you intend by arisch. I am not of Aryan extraction: that is Indo-Iranian; as far as I am aware none of my ancestors spoke Hindustani, Persian, Gypsy, or any related dialects. But if I am to understand that you are enquiring whether I am of Jewish origin, I can only reply that I regret that I appear to have no ancestors of that gifted people."