My stepsons are now 16 and 17 and while it seems to have gotten a little better, they were like that since I've known them (at ages 5 and 6). They would argue and bicker over the dumbest things imaginable. One time it was over where exactly did Luke Skywalker get his arm cut off in Star Wars. Or over the rules to a board game, even when the rules were explicitly spelled out in the instructions. Or who had to put the cereal back (the one who took it out in the first place or the one who ate from it last?). Or the younger one flipping out because the older one had a imaginary plate of cookies, and pretended to eat all the cookies. Really?
I think so much of it had to do with them being boys, and only being 13 months apart and being together all the time. And their mom used to compare them in front of each other, talking like they weren't even there and couldn't hear her and weren't paying attention, and I'm sure that did not help either. I found myself many times just telling them, "Look, you are driving me and everyone else crazy, just knock it off!" It was just that frustrating.
Now that they are in high school, and have started acting more like individuals, it seems to have lightened up. For now, like someone else suggested, I would just put their names on everything that looks the same (cups, etc.) You can also keep a chart and keep track of who does what when and whose turn is it next. But don't expect them to get along and like each other every day - they will love each other tremendously but if they are not allowed to have their little disagreements and are expected to always get along, they could end up really resenting each other. As long as it doesn't escalate to bullying, name-calling, getting physical, etc., I would not intervene. Sometimes they have to figure out their own solutions.
When my cousins were little, if they really got into a fight with each other, my aunt and uncle would make them sit on the couch and hold hands without talking. That cut down on the fighting real quick.