Continuity mistake: As Thorin is picked up by the eagle, the eagle's talons roll him towards the camera. Both of the eagle's feet are in view and you can see all the way down Thorin's body to his boots. Orcrist is nowhere on his body during this initial shot of the pickup. As soon as the shot changes (where the Oakenshield drops free) and both of the eagle's feet come back into view, Orcrist is now on Thorin's body, running over his stomach and left leg. Had it been there before, it would have been visible when the eagle rolled him towards the camera.
Other mistake: In this movie, Gandalf looks older than he does in his grey incarnation in Lord Of The Rings: The Fellowship Of The Ring. However, this takes place before the Lord Of The Rings trilogy, so he should look younger, or the same.
Continuity mistake: In the scene where Bilbo spares Gollum's life, Gollum turns around facing the invisible Bilbo and extends his right hand out to a rock. The far shots from in front of Gollum show his arm almost fully stretched out and his hand away. But the shots from behind Gollum show his right arm bent on the rock with his hand much closer and level with his head.
Continuity mistake: As the group reaches the dilapidated house that Gandalf claims belonged to a farmer, a birdhouse on a pole can be seen on the threshold. In the next shot, it is gone.
Other mistake: When giving Sting to Bilbo, Gandalf tells him it is an Elven blade and will therefore glow blue when Orcs are near. However, Glamdring and Orcrist are also stated to be Elven blades, but they do not glow blue.
Other mistake: Just after he arrives at the gathering Thorin states that he wouldn't have found Bag End had it not been for the mark Gandalf made on the door. Bilbo then claims that 'There is no mark on that door, it was painted a week ago'. However in the earlier scene where Gandalf makes the mark the paint work is cracked and weathered, more than it would have done after only a week.
Continuity mistake: When Bilbo brings the two bowls of stew for Fili and Kili there's a spoon in each of the bowls, but after Bilbo sets down the bowls one of the spoons has vanished when he picks up the bowls again in the closeup, but the spoon reappears when they run after the Mountain Trolls.
Revealing mistake: When there is a flashback of Thorin in the war, in the first few seconds, on the left of the screen, there is a man with a shield. He swings it at an ogre and you can see it misses by a good five inches, but the ogre moves his head back as if it were hit.
Deliberate mistake: When Bilbo finds The Ring, he kneels down to get it. In the prologue in Fellowship Of The Ring, Bilbo is lying on the ground. The direction he looks toward when he overhears Gollum is also different.
Continuity mistake: In the scene with the mountain trolls, the captured ponies are in a corral untied. Over the course of the entire troll scene, the horses go from being free in the stall to being tied up by the reins.
Continuity mistake: At Bag End when the Dwarves begin to burp, it shows one of the younger looking ones laughing next to another Dwarf and sitting down. The very next shot cuts to show that same Dwarf now standing and letting out a huge burp.
Continuity mistake: In the Fellowship of the Ring, Bilbo was old when he found the ring. In this film, he is young when he finds it.
Continuity mistake: The mark that Gandalf puts on the door (that looks like a capital F) changes. When Dwalin arrives, there is an additional part of a line on the second line of the capital F. But when Gandalf made it that additional part was not there.
Continuity mistake: In The Lord of the Rings, when the map of Lonely Mountain is shown, it says "Here of old was Thrain king under the mountain" (referring to an ancestor of Thror and not Thorin's father who has the same name and was never king under the mountain). But throughout The Hobbit, the map instead says "Here of old was Thror king under the mountain."
Suggested correction: Thrain was king after Thorin. The map would have been updated after Thrain's death, and he was subsequently buried there.
Thrain II was king after Thorin I and father of Thorin II (Oakenshield), but as said he was never king under the mountain but was king during their exile, Thror was the one who went back to Erebor to sit on the throne again until Smaug sacked it. The Thrain mentioned on the map is Thrain I (father of Thorin I), who is the founder of the kingdom under the mountain after Durin's folk were exiled from Moria by the Balrog (Durin's Bane, Durin being Thrain I's grandfather).
Also, even disregarding that, it is impossible for the map to have been updated to say a different dwarf's name, because the map is given to Bilbo at the end of the trilogy, and the ending shows a close-up of the map with "Thror" still written on it, whereas in the LOTR trilogy, where we see the exact same scene of Gandalf arriving at Old Bilbo's house (albeit from Gandalf's point of view rather than Old Bilbo's), Gandalf sees the map and it says "Thrain" on it.
Continuity mistake: After Bilbo has written the prologue to his book, Frodo is talking to Bilbo and then heading off to wait for Gandalf's arrival. This contradicts the extended edition of The Fellowship of the Ring, where Frodo is shown to have already left the house to wait for Gandalf before Bilbo begins writing his book (which he begins with a section called "Concerning Hobbits," which he states is "where to begin," indicating that Frodo left the house before Bilbo wrote any of the book).
Other mistake: When an invisible Bilbo is about to jump over Gollum to exit the cave, you can see Gollum prepare himself for impact just before Bilbo jumps over him. This isn't logical if Bilbo is invisible.
Continuity mistake: At Bag End, Bilbo recovering from fainting, sits in an armchair. Gandalf is speaking with him. Behind Gandalf is an alcove with an unlit candle, which is lit in the next shot, although not illuminating any of the alcove, then it's unlit again.
