I think its irresponsible to wear hospital attire anywhere but in the hospital.
Imagine what gets on your coat and scrubs in a typical day, especially if you are the student/intern/resident.
Would you want someone who works at a meat packing plant or in a vets office wearing their soiled uniform while you stand behind them in the line at the bank?
I wouldnt.
I have seen people in the medical field, nurses to physicians, wearing their uniforms in places like the grocery store. I realize that convenience of going home and changing isnt always easy, but at least remove the coat, stethoscope or scrub top...and try to throw on a T-shirt to contain some of the festering goodness on your clothes.
With that said, I know many residents who throw their white coat over the passenger seat back with their name and title conveniently showing...some say its in case they get pulled over for speeding while Im sure others do it to impress people next to you in traffic. Afterall, nothing says "sexy" like a young doctor in a white coat...driving his Toyota Corrolla.