The Promise

Azul is Spanish and Portuguese for blue, possibly a reference to Azula's Firebending.
Her name may also come from the Sanskrit term Asura, a Hindu term for demon.
Azula's name was originally going to be "Zula".

In some Avatar comics, her name is mispelled "Takara" instead of "Katara".
Katara's voice actor, Mae Whitman, has previously played the part as Rose in American Dragon: Jake Long.

The Southern Air Temple is the only episode in which the title screen, which denotes the chapter and book, does not have a white background (the background is the sunrise).
According to the Nick.com's website...

I feel as though a lot of people are under the impression that Ozai treated Azula nicely. Yes he did indeed buy her all these nice things but at the end of the day she was pretty much just a pawn to him. Azula may have had her father's respect, but it didn't seem like she had his love.

While yes--as far as we know--Ozai never put his hands on Azula, the verbal abuse was apparent. She is afraid of him. Whist we haven't really seen him abuse her verbally I think it was hinted when he yelled at her before declaring himself the phoenix king. I also couldn't imagine he let her down easy behind the...

First and foremost, I am not by any means a professional (I think that's a given though) this is simply my sort of speculation and opinion as to what she'd be diagnosed with based on what knowledge I have of psychology. A lot of the following quotes and information will be pulled from my abnormal psyc textbook and will be cited in MLA format (because I'm a dork like that and I'm used to it).

Schizophrenia

There are actually a few disorders I could see her having some less so than others. But above all I would diagnose her with schizophrenia...above all the paranoid type. "People with paranoid...