Roy is a complicated man. Ten minutes with him will tell you nothing about how he really is, and most likely will leave you more confused than you were already. The truth is, Roy chooses who he wants to be known by. He plays an act for bystanders, which is basically his way of keeping people from getting close to him, while at the same time concealing the true motives behind his actions. But the ones that get to see past his masks (even if only a little), those are the ones that find himself entranced by Roy and, somehow, can't leave his side after that.
One of the characteristics that shine through Roy it's his determination. He's not one that gives up at anything, and follows his convictions till the end. He's got a keen sense of leadership, something provided by the great respect he can command, from both his allies and enemies. And besides being smart (one just needs to take a look at the success rate in his job and his undercover business), his intelligence is also obviously far above the average. Not only he can bring undying loyalty out of people, but he in return is also loyal to them, and to the duties he's given to himself.
Roy learns from every experience, every encounter and every win and loss. He's not the kind of person to brood and live in the past, his eyes are always set in the things that are to come, in the future. No matter how hard to climb is the next wall ahead of him or how deep he's fallen, Roy always goes on. He's got the ability to influx strength and hope into the people around him. He's a visionary.
Roy is an extremely polite person. He treats people with the most respect, be them older or younger than him, whatever their sex or race, doesn't matter how much or little he knows them. However, he tends to be not very straightforward. At least not with the common use the word "straightforward" has. Roy likes to be careful with words, and uses the language as delicately as a poet would do. Most of the time, there's much more meaning to his words than those of any other person. It takes time and experience to know what Roy Mustang is really talking about.
Ironically, Roy is not more misunderstood by other characters, than he is by the this series' fandom, in my opinion. He's often regarded as a cold, smug, arrogant, manipulative man. Honestly speaking, I don't know what the hell they're reading.
In fact, one of Roy's main characteristics is that he is not manipulative (at least towards the people he considers his friends or allies). He always makes sure everyone knows what they're getting themselves into and that it's completely their decision. Of course there are times he hides some information from them, but it's never out of malice, but because he considers it best.
Roy is not cold. He may appear very serious or strict to outsiders, but he is candid and warm with the people he cares about and never doubts to offer a helping hand if the situation calls for it. He gets worried sick if someone he loves gets in danger (especially if it's because of him), and will go to whichever extent to protect them. Roy is not only passionate about his goal, but also about taking care of whoever may need it.
Roy is not an arrogant bastard (or smug bastard, pick any of them). So yes, he usually projects confidence wherever he goes, but that's because he knows the limit of his abilities. Also, because the job calls for it. He's a natural-born leader, and thus he can't be showing weaknesses so easily. Roy, in fact, has no problem in admiting he's not skilled enough to some duties, but takes pride in knowing he's an excellent alchemist who does a good job most of the time. He can value danger situations and act in accordance to them, whether it's retreating, attacking or something else. Actually, Roy has an inner self-loathing habit, which is mostly due to his experiences during Ishval.
It bothers me that some people can go as far as to imply his moral values don't seem all too clear. Roy is not morally neutral or even remotely close to it. His goal was set even before he encountered the Elric brothers and he can tell perfectly what's bad from what's good, that's what got him into this mess in the first place. However, no matter how strong is his resolution to attain his goal, he will not take innocent lives to reach it.
Often labelled also as a lazy bastard, a deeper look will tell you that he really is not. So yes, he enjoys procrastination and tends to leave paperwork to the last minute, but that's hardly a proof of not doing his job. The truth is, Roy was greatly valued by his superiors in East City (that is, the ones who don't get irritated by his fast climbing through the ranks) and was assigned a lot of work due to his and his team's efficiency. There's not a single moment when he's shown not working, digging out information or similar. I don't think one can get so high up the military that young without working hard and being good at it.
And what's with the whole "he's obsessed about miniskirts" thing? I've got four words for you: it was a 4-koma. Funny how little things like these get to the fandom, they somehow get twisted and then everyone takes them from granted because no one cares about finding out who a character is by themselves, without any outside influence. Please.
