When Gandalf leaves the Company outside Mirkwood Forest in the digital rain, only Thorin's hair is wet.
Beorn still wears a shackle on his wrist from his time of enslavement by Azog. However, the shackle is too small to fit his arm in bear form, nor was it present when he was a bear the previous day. He should have already broken free of it.
When Gandalf fights Azog at Dol Guldur, his sword falls from his hand and he is thrown backwards. Immediately afterwards, his sword is sheathed at his waist, despite the fact that he is now holding his staff in both hands and could not have sheathed it.
At The Prancing Pony in Bree, the food on Thorin's plate moves around in various shots although he is not eating but talking to Gandalf. Also the cheese on his plate disappears and then reappears.
When Azog calls for Bolg in Dol Guldur there is a side shot of the two approaching each other where Bolg is clearly taller than Azog. When they are speaking in the close-up Azog is looking down at Bolg implying that he is taller.
Gold melts at 1,948°F (1,064C), yet Thorin can ride on a river of molten gold, extremely close to the level of the gold itself, without suffering any burn damage.
Molten gold's color is not actually golden.
At the furnaces, when Thorin taunt Smaug into breathing fire to start up the furnaces, there are plenty of wooden objects (benches, crates,...) in the path of Smaug's fire breath, that will not burn, yet the coals in the furnace almost instantly catch fire.
When eight Dwarves tug on one spider to remove its legs, all eight legs come off at once. In reality, at least one leg should have remained attached as the pulling force in the other directions would have ended.
A Thrush is not nocturnal. Primarily, only owls will be out in moonlight.
The Orcs attack Bilbo and the Dwarves shortly after they escape the wine cellar in the barrels; as if they were waiting for them. Since the Orcs were unable to gain entrance into the Elven kingdom, there is no way they could have had any knowledge of when Bilbo and the Dwarves would be coming back out or where they would be escaping from. The Orcs had surrounded the kingdom and intended to wait as long as it would take for the party to come out.
When Kili is looking at his rune stone, in the close-up shots, Aidan Turner is not wearing his prosthetic Dwarf hands.
Just after Thorin rides down the river of gold on a wheelbarrow, Bilbo is forced to leap off of the falling bridge knocked over by Smaug. Upon hitting the ground, he rolls and Sting at his side can clearly be seen to bend almost at right angles, indicating a rubber stunt sword.
As the company prepares to enter Mirkwood, the skies become overcast and it begins to rain. During this scene, there are shots of Gandalf where light and shadows show that he is standing in bright sunlight instead of overcast skies, with digital rain added in after filming.
Robert Kazinsky, as Fili, can be seen in some shots of the film, most noticeably when the Dwarves are about to hit the first waterfall after escaping from Thranduil's.
In the opening scene there is a cast iron well pump in the alley that is more suited to a twentieth-century farm in New Zealand than to a Roman-era civilization.
When Bard arrives home, Tilda greets him, but her mouth doesn't move.
The Wargs have paws, yet when the Orcs ride them away from Laketown, their feet clop like hooves.
The movies previously retained the idea from the books that sunlight renders Orcs non-functional. Gandalf remarked in The Lord of the Rings: The Fellowship of the Ring (2001) on how alarming it is that Saruman's breeding program has produced sun-resistant Orc soldiers. Yet in the barrel escape scene from Thranduil's caverns, the orcs are chasing the dwarfs down the River Running, and doing hard battle, in broad daylight without suffering any ill effects.
In the treasure vaults of Erebor, Smaug tells Bilbo that he'd almost be willing to give the Arkenstone to "Thorin Oakenshield" just to watch it drive him mad. Smaug has no particular reason to know the name of the grandson of the king he deposed from Erebor, and since he's been sealed inside the lonely mountain ever since, he certainly wouldn't know the "Oakenshield" name that Thorin earned in a battle at Moria years later.
In the extended edition, Thrain tells Gandalf that Sauron and Smaug are already in league. However, Sauron is confined to Dol Guldur and nobody has entered the Mountain yet, so there was no way for Sauron and Smaug to communicate, and as Thrain had been a prisoner for years it's not clear how he would know of this.
Thorin tells Gandalf that his father Thrain went missing in the battle of Moria and was later seen wandering the woods near Dunland. In the extended edition Gandalf finds Thrain was captured and taken to Dol Guldur, and there's a flashback to the battle of Moria where Thrain is overpowered by Azog. This doesn't line up with Thrain being seen alive after the battle, as Azog had him at his mercy and had no reason to let him live.
When Thorin and the rest reactivate Dwarves' forges in Erebor, these melt the gold contained in them in a few minutes in order to create a golden giant statue as a trap for Smaug.