Recent discussions about alignment in a couple different locations brought up examples of some of the same ol' problems we always see in such discussions: lack of agreement, concerns over the ambiguity of some definitions, monolithic treatment of monster personalities. Now, I've gone on record before about how many different ways there are to interpret alignment, and I still say you are free to pick the one that works for you. However, I'm coming to the conclusion that alignment as alleigance to a side in the cosmic battle is in conflict with alignment as a personality guideline, and many of the problems with alignment come from trying to do both at the same time.
Let's start first with the obvious: animals vs. people. Animals that have an innate alignment can't possibly be making a philosophical choice to side with one faction or another. Either their alignment just reflects a behavioral tendency (which kind of undermines the whole cosmic battle theme, plus it means they can be trained to behave differently,) or it reflects a taint: they have been chosen by Chaos or Evil to play some role. Either way, this is at odds with people choosing an alignment out of religious belief, and it doesn't fit with tracking the alignment drift of player characters or rewarding good alignnment roleplaying.
Beyond that, you have conflicts when you try to interpret Law as both the pro-god/pro-civilizatiion faction and the regimented, orderly personality, and Chaos as anti-Law as well as disorderly and rebellious personality. Should the forces of chaos form organized groups to oppose Law? Should people who support creativity and freedom of expression be part of an open rebellion against the armies of the righteous? Just what is a Chaotic personality? Many people are unclear as to what Law/Chaos mean and call it a meaninglessly vague alignment axis; I'd say that this is because Law/Chaos work better as factions, with no presuppositions about personality, than they do as behavioral guidelines. Conversely, Good/Evil work better as opposed personalities or behaviors; if Evil is a faction, we wind up with dastardly comic-book villains who openly call themselves "evil" while twirling their moustachios.
You can use Law = supports the group and Chaos = rebels against restraints as a shortcut behavioral guideline for the nameless masses of the opposed armies, but any character the players interact with on more than the fight/flee level should have a really personality, not linked in any way to those stereotypes. Chaotic forces may be anal-retentive task masters, calmly organized gentility, free-spirited hippies, selfish thugs, mocking rebels, or many other personality types, some of which may also be common among the forces of Law.