When we first see Gmork (the wolf) in his cave (at around 5 mins), his teeth are close together and short but when we see him talk to Atreyu (at around 1h 12 mins), his teeth are now further apart and longer.
When Bastien and his father are talking at breakfast his father drinks about half of his egg drink (at around 43 mins) before sitting down (at around 56 mins), later when he picks it back up again the cup is about three quarters full again (at around 47 mins).
A Z-shaped reflection can be seen floating around the left side of the picture as Bastian is on Falkor's back pointing out Atreyu on the ground. This probably refers to a slowly rotating long, skinny, Z-shape like a grass stem or branch just in front of Bastian (center screen at 01:29:03) as Falkor flies toward Atreyu just before Bastian points at him.
After Atreyu leaves Rockbiter (at around 1h 10 mins), he walks away from the camera in a long shot along a path with broken and fallen columns to its left and right. As a fissure opens beside him the camera cuts to a medium shot at (at around 1h 10 mins), but now there is a large wall of rocks to the right of the path. (at around 1h 10 mins) the camera cuts back to the long shot where the broken and fallen columns are again to the right of the path.
Toward the end of the movie while she is speaking with Atreyu, the middle two rows of beads in the head piece that the child-like empress is wearing, change position between closer together and further apart from 81:00 to 85:00 on the DVD.
The knight's staff lands on the right Sphinx's foot once he falls off his horse, but later on when Atreyu is attempting to cross the gate, the knight's staff is laying parallel to the knight's dead body.
When Atreyu is in the Swamps of Sadness with his horse, the horse sinks because it gives into the sadness, but Atreyu doesn't sink, even though he is crying and sad that his friend has died. Though not properly shown in the movie, the book explains how AURYN is protecting him. (His eventual near-sinking at the end of the scene, which never occurred in the book, is due to the plot changes that were made for the movie.)
In the scene where Falcor delivers Atreyu to Engywook & Urgl, Atreyu is clearly much larger than the small, old couple. Later, when Engywook and Urgl are standing on/near Falcor they they are about the same size as Atreyu in relation to Falcor.
In the wide shot from 50:53 to 50:57 on the DVD where Atreyu scales the mountain to look through the telescope at the first oracle, you can see a horizontal line where the set wall (lighter blue) and ceiling (darker blue) meet. Basically, you can see that they are in a room instead of out in the desert.
When the Night Hob reaches the Ivory Tower he is seen pulling himself up through a gap in the Tower. His Bat appears via an adjacent gap. They are meant to be at the top of the Tower, and yet behind them is a visible blue screen, not clouds nor the sunset (at around 23 mins).
Just as the armored knight drops dead off the horse from being shot by the Sphinx Gate, his metal staff lands on the right Sphinx's foot, which bounces as if it was made out of something other than stone.