I never understood why Starfleet would have different badges for each ship. Was this idea derived from the different mission patches NASA used?
I think it was a staging trick, a small-screen signal to the audience that a character was in Starfleet but not an Enterprise crewman. It helped delineate the us-versus-them drama with Commodores Stone, Decker, and Stocker, and Captain Tracy. "This guy is with us but not of us."
The distressed shirt color on Exeter's doctor helped symbolize the drama of a whole crew slowly dying.
Bernie looks just like one of our managers here at work.