Canonically, Azula is extremely perceptive about people... within certain parameters.
She's good at recognizing when somebody is lying, albeit not as good as an Earthbender- she does it through good old-fashioned perception and attention to details. Little things don't tend to slip past her. However, she does have raging emotional blind spots that she refuses to acknowledge (she tends, for instance, to assume altruism is always either naive or self-serving due to her unrelentingly cynical and paranoid nature.) As such, it's very possible for her to Miss Things that she shouldn't purely because she dismisses them, misinterprets them, or fails to correct for them.
If you have any details for your character that you would like Azula to notice or deduce, feel free to present them here. If you specifically think there's something here she would misread entirely, feel free to point it out as well. You're also free to opt out entirely- it's completely possible for Azula to simply write your character off as not worth noticing in finer details. I'm flexible, this is meant to be fun, not OP!
(Please also indicate if this applies to specific games or all interactions with your character. I'll do my best to keep track, but that will make it easier for me!)