In the scene with Sokka and Katara, just before Sokka is breaking the ice. You can clearly see a large ice formation just behind and the the left of them. During the ice breaking scene it is still there, yet when the ice is cracking and they back the way they came its gone. Also, in the over head shot the terrain all looks flat.
During the scene where Aang is being tested by Zuko's uncle Iroh, Iroh pours a cup of water onto the table and it coalesces into a circle (at around 26 mins). In the next shot, Iroh places a rock on the table where the water had just been (at around 29 mins), but the water has inexplicably disappeared.
When Aang and his friends are arrested in place where is occupied by firebenders, they are put into a prison for earthbenders. However, the entire prison is made out of earth, as Aang points out, to which they should have known this already, defend themselves and escape.
When Zuko takes Aang onto his ship, Iroh puts a rock, lit candle and water in front of him, to which all three pull towards him, showing he is in fact the Avatar. However, Aang walks by several rocks, water and fire and they never react to him, without bending.
During the first conversation between Fire Lord Ozai and General Zhao we can see that Ozai's eyes move from left to right while he looks in the direction of Zhao's chest, thus revealing the use of a prompter.
When the flying lemur jumps on Aang's shoulder, Aang's hands supposedly touch and pet the Lemur. But it is clear that the lemur is computer generated as Aang's hands do not actually touch the creature, they seem to hover about an inch or so above him.