Immediately before Bofur throws the egg to Bombur in Bag End, Fili is sitting to Bombur's left. When he catches it, Ori is sitting there.
Throughout the goblin scene and the scene after with the orcs the sword Bilbo has only glows sometimes even though it was stated early it is supposed to glow whenever orcs or goblins are around.
When Bilbo is attempting to save the ponies from the trolls, the real horses are bridled and tied to the posts. When the ponies are computer-generated, they are loose and unbridled.
As Thorin addresses the group at Bilbo Baggins' dinner table, the arrangement, color, and texture of items in a plate (cookies or biscuits) changes.
In the first scene with Galadriel, her tiara is off center. A moment later, it is perfect when you see her again.
Sting, the elven blade which Bilbo was carrying in the Goblin City encounter, glowed blue even after the fall to the bottom of the chasm under the City because Gollum had dragged away a barely alive goblin in hopes of eating it. Once Gollum killed the goblin, Sting's glow disappeared.
When the party is captured by the Goblins and Bilbo crawls away, a Goblin's CGI foot passes through the bridge he's walking on.
Early in the journey, as the Dwarves, Bilbo, and Gandalf are riding in the rain, none of the characters are really wet. In the downpour, water should be streaming down Bilbo's face and off of Gandalf's hat and beard.
The handle of Bilbo's round entry door is in the center of the outer side of the door. However, the lock is on the edge on the inner side and no mechanism can be seen linking the two together (the door is made of wooden planks, single layer thus it is not possible for such a mechanism to be hidden inside the door plate).
Gandalf's contacts are visible in close-up shots, particularly scenes around the table at Bilbo's.
(Extended Edition) The first scene in which Bilbo Baggins rides his pony there is a brief moment when the white on the horse's nose becomes transparent. This is a Chroma key mistake, the technique used to remove green (or blue) screens. When set to high it also starts to affect white.
During his stay in Rivendell, Bilbo comes across the mural depicting Isildur and Sauron, showing Sauron wearing the One Ring. In the Fellowship of the Ring, Boromir observes the same mural, showing Sauron without the One Ring.
When Thorin and Company look over Mirkwood and see The Lonely Mountain, it is about 300 miles away. On this planet, even from a height, seeing 30 miles is nearly impossible. For the Cast to see 300 miles would require the planet where Middle Earth exist to be 10-15 times the size of Earth.
The scabbard for "Orcrist" is split down the edge side because the tip half of its blade is wider than the lower half towards the hand guard - when Thorin (partially) draws the sword after he finds it in the troll hoard, his fingers are wrapped around the split, putting him in severe risk of cutting himself (you can clearly see the wide part of the blade emerging from the split under his hand). A seasoned warrior like him would not make such a mistake, even if the straight dwarven swords he's used to don't have this feature.