I got to thinking about this when my wife rolled up a wood elf fighter the other night. We hit a small bump, and I wanted to share this experience to gather thoughts on the subject and hopefully make things smoother for others.
She likes to roll dice, so naturally when she got the opportunity to roll for her soldier's background of Ideal, she did so and rolled Might - In life as in war, the stronger force wins (Evil). For Flaw, she rolled "I obey the law, even if the law causes misery."
Ok, so the natural way to take that is definitely Lawful Evil.
After that, perhaps a bit out of order in the process, she read the alignment descriptions and promptly selected Chaotic Good as her alignment.
I had to stop and think about that one.
Yes, I can see that.
You could pull it off but it would require an extraordinary role player and even then I think the situation is unstable and the character is heading for a fall. There is inherently nothing wrong with the idea of a character that believes that they are one thing when actually they are the other. Javier from 'Les Miserables' believes he is Lawful Good, and even that Lawful Good is the highest good. In fact, he's no more than Lawful Neutral and blind to his on condition, and the author is asserting through the story that law while required in some situations for good ultimately detracts from goodness (a neutral good position), notably having characters break otherwise firm moral codes when necessary obtain a higher purpose. So ultimately, even Javier's aspirations to Lawful Goodness are judged unfit by the story.
You could pull off the contradiction above only by stretching the language and pulling some sleight of hand. You could have the character be personally loyal on account of friendship to a person who everyone knows is a vicious tyrant except the loyal character. In this case, the character is loyal 'to the Law' in the sense that the law is a embodied in a person. That person however rules by capricious and cruel whims. The character is continually justifying to herself the rightness of what she is doing in terms of friendship, personal loyalty, and 'the big picture'. She legitimately believes she's obeying the tyrant out of personal love and affection (that she may or may not wrongly assume is reciprocated), and to prevent more serious evils from happening.
In fact, she's utterly blind to the fact that the real reason she's obeying is that she is a subservient sycophant who is intellectually and emotionally conditioned to obey and never really questions hard why. Additionally, she is blind to the fact that the real reason she carries out the king's vicious orders is that she enjoys it. She enjoys stomping her boot down on the weak, and she lies to herself and says they must deserve it.
Of course, at the beginning of a story she's in a moral crisis - even if she's blind to it. She can't continue down this path forever while still maintaining her innocence and sense of an independent self. At some point she's going to have to confront her flaws and subvert them, or else she's going to cease to actually have a naturally good and independent nature (even if she's not aware of the change). As the demands of the tyrant become greater on her, she's going to have to break one way or the other.
There are a couple of other ways to go with this, including pretty much the opposite of the above scenario with person living out their flaws without realizing they are doing the job badly because they don't really believe in it, but that's an example. The point is that when you put that sort of tension between what you believe in your heart, and how you actually act, it's going to be explosive and its going to have to require someone that can juggle and walk tightropes at the same time to pull it off convincingly.
I welcome the traits, ideals, flaws, and bonds and Inspiration...I think it's going to be a much better for encouraging roleplaying than alignment alone, and I like that alignment can conflict with some ideals/flaws/ etc to create more interesting characters, but I feel like that's not something they intended, and in fact had intended that they match.
I think that from the sound of it we are (finally) moving in the right direction with official alignment. Alignment alone works just fine when you work out alignment from your traits, ideals, flaws, bonds and inspirations implied by your background, or vica versa work out what it means to be a particular alignment by assigning your character flaws, ideals, bonds, and inspirations. It's just that the system never really encouraged you to do that, and as such was something you only saw at particular tables. If anything, I'm more than a little worried about having firm mechanical beliefs as flaws, and hope there is a means for trading them out as your character evolves over time.