For present day/newish military history, keep the impression that you are assuming, reasonably generic. Some units are more sensitive to this than others, as to how their image is portrayed/imitated/stolen under false pretense. A good example of this would be ex-RCR members - i've heard that they don't take too well to others wearing a maroon beret and other accoutrements related to that regiment. Don't assume rank insignia that you haven't earned, or field awards/qualifications that your own sweat and blood hasn't earned.
There is a clear, but fine line between assuming a persona/look in terms of gear for airsoft/paintball purposes, and impersonating someone/some unit that you clearly are not in real life down to rank, insignia and attitude. One is good, the other, definitely not.
Beyond that, you should be good, IMHO anyway.