Corrected entry: After the fellowship passed the statues of Argonath, the river ends by a huge waterfall. There's a huge rock on the very tip of the waterfall, yet the reflection is not visible on the water; compare it with the Argonath statues which have its reflections on the water.
Corrected entry: The doorknob to Bilbo's Hobbit hole is in the center, as mentioned in the books. However, the interior doorknob is at the side of the door, in the normal place.
Corrected entry: When Sam tried to follow Frodo (at the very end) and started drowning in the Great River, Sam was all the way under water. Frodo saved him, and then when you see that they are both in the boat again, Sam is COMPLETELY dry. Only his head is dripping wet. Frodo also reached in to save him, and Frodo's arm wasn't wet, either.
Corrected entry: When the Fellowship is running through the mines of Moria, after they have fought with the orcs and cave troll, they reach the bridge of Khazad-dum. Then they are stopped again by the great number of orcs. When the Balrog arrives, they run further to Khazad-dum; the filmmakers used the exact same shot for this scene as when the Fellowship was running from the orcs in the first place.