The Henry is more period correct but still a stretch placing the show in pre Civil War. The patent wasn't applied for until late 1860 and they really didn't hit the field in any quantity until 1862. Still pretty minor compared to what Hollywood usually does.
Leadcounsel, I would imagine there might be some discoloration but no serious damage. I would think it would a handy way to carry extra rounds while on horseback which would be the advantage.