Let me preface this by saying that I absolutely love Avatar the Last Airbender. The characters and world are phenomenal. It's a satisfying case of action-adventure wine being put into a very appealing bottle.
Having said that I have noticed some plot holes. The biggest has to do with Zuko. His two overriding characterisitics are his ardent loyalty to his mother and his misguided loyalty to his father. The two intertwine in the episode "Zuko Alone" to create a very puzzling situation.
We know that Azula warned Zuko that Azulon was planning to have him killed as punishment for Ozhai's callous jockeying for the throne in the wake of Liu-Ten's death. We also know that Zuko is aware that the Fire Nation was complicit in his mother's disappearance. (When he tells Katara that they both lost their mothers due to the actions of the Fire Nation.) We also see Zuko run to his father after Ursa leaves and throws at him this question: "Where is she?"
The fact that Zuko confronts his father would seem to suggest that maybe he thought Ozhai had something to do with the disappearance. This renders Zuko's subsequent devotion to his father completely inexplicable, doesn't it?
So whaddya think? Am I over-analyzing this? Your comments are appreciated! :)