In all honestly, what happens on the field happens between airsofters; soldiers don't randomly drop by to check out if anyone is imitating them too closely for their liking. As mentioned, avoid wearing specific items that you haven't earned: ranks, awards/ribbons, skills, unit, etc. There IS fine line between dressing-like (impression) and impersonating that must be respected.
So the only real issue is what you'll be doing with all that kit off the field: will you be plastering pics of yourself all decked out with medals and ribbons on your FB page? Going to the mall dressed as a serviceman? Making any sort of claims you aren't entitled to?
If none of the above, then it's a moot point. Don't be a bonehead and it'll be fine.
The Lerch example that was brought up and -- while I think the arsse folks are full of themselves and only succeeded in demonstrating how empty their lives are -- that's a direct result of those pictures being out there for the public to see. Was he just happy to show off his impression/collection? Probably. But without proper context/framing ("This is an impression" "I am doing this to illustrate the various pieces of kit from a given era" etc) I can easily see how it can be taken the wrong way. And honestly the public at large doesn't need to be exposed to this.