I'm ok with museums displaying copies, fakes, dummies, reproduction etc., so long as no attempt is made to pass them off as the real thing. Some things I would expect and demand to be fakes or dummies, simply for safety reasons.
(for example a display of 1880s mining should NOT include real, live, 1880s dynamite.)
to date, I haven't personally met any museum people who would not listen to friendly "corrections", once they have accepted your bona fides. "I was there and this is how we did it" really isn't enough. Proof through photos, or being part of an official group (vets group), or being a published author on the subject, etc, things like that, which back up your word are good to have, and get you listened to.
Tell them that the vase belongs in the 5th dynasty and not the 7th where they have it, you better have valid bona fides. Also remember that for some things, reality has to fight an uphill battle against generations of TV & movie misrepresentations.
I forget which (bad) movie it was, something set in the Pacific theater, where the sgt hangs grenade(s) off his web gear, and snags something, pulling the pin. He realizes it, just in time to utter a bitch about dying because of a "stupid cherry mistake!" then, boom! (me, I like to think I would have thrown the grenade, rather then spouting a line, but hey, its a MOVIE)
Another thing to consider is that if something isn't technically right, but looks right, they may go with it, over what really is right. One complaint from a real expert once in a while, vs. constant complaints from people not seeing what they expect to see would make a difference to an administrator with a bureaucrat's, and not a historian's mindset.
Of course, if you run into "we are the mighty (infallible) Smithsonian, and you are a peon" attitude, getting things right will be an uphill battle.