My experience is that the mechanic is more subject to mistake or misunderstanding than to interpretation - not remembering the order of operations, for example, can make things weird.
The individual aspects are subject to interpretation. This is by no means a bad thing, more often a feature than a bug, in my experience.
For example, in a Dresden Files game I occasionally play in, my character is a musician. For thematic reasons, I tried to phrase several of his Aspects in term so song lyrics. One of them is from Hotel California, "You can check out any time you like, but you can never leave." The character has former entanglements with Fae powers, and I put it there so the GM could compel me to keep me entangled (or, I could ask for an occasional fate point when I willfully failed to try to extract the character from fae business). It is an instance of an aspect that I would now call poorly phrased, as it is difficult to see how it could be used to invoke for a bonus or reroll.
However, the GM is a bright and creative dude, and he saw a way - a different interpretation. That phrase doesn't just represent the character's fae entanglements, it represents an even larger theme - the fact that his life, and everything in it, is tangled, and once you're in the web, it can be hard to get out. So, when he's in a fight, or a social encounter, I can often invoke it for a bonus on actions that are trying to keep the enemy from escaping.
Not quite. Note that the aspect, in and of itself, *never* merits a mechanical reward. In FATE, it is not enough to behave consistently with the aspect (or alignment) to get a fate point. That behavior must also complicate the character's life to a significant degree. Bloviating religious dogma isn't enough - you have to cheese off the shopkeeper with your bloviating, such that he won't sell you the new weapon you kinda needed.
Actually, the difference between aspects and alignments is important here, as others have noted.
If, in FATE, at a given time, the GM doesn't think you're really in line with your Aspect, you fail to get a point that'll give you a +2 on one die roll. It isn't really worth an argument. There' will be more opportunities - heck you may be able to immediately ask if another Aspect applies instead.
In D&D, if the GM thinks you've seriously deviated from your alignment, your cleric character could, for example, lose all spellcasting power! Alignment stakes are often much larger than Aspect stakes, so are more likely to become arguments - the player has a lot more to lose.
There are mechanics in FATE that can mirror the major loss from deviation from alignment (called Consequences), but you can't just assign a big consequence for no reason, or for not playing to one aspect. Such a consequence would be the result of some major failure for the character - he can take the consequence instead of damage in a conflict.
