Continuity mistake: When Fili and Kili arrive, the door is left open. We never hear the door close, yet it is closed when Bilbo goes to get the door for Gandalf and the other dwarves. (00:19:00 - 00:19:40)
Suggested correction: So... What's your point? I can, and I'm sure you can, close your door without making a sound. Plus the scene isn't one continuous shot so there is no reason it couldn't have been closed off camera.
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.
