When Goldman and his girlfriend go out to dinner, she's got way more hair on her, wearing a massive blonde wig of hair that is supposed to look real but is not consistent with how she really looks.
During the season one finale when the medals are handed out to the platoon, the soldier awarding the medals referred to Purcell as Private 1st Class. Purcell's rank since the beginning of the show is Corporal - which is higher.