The murder investigation of an active duty Marine should have been handled by military authorities, not civilians.
Enlisted personnel in the USMC would not have been called sir, only officers are referred to as sir. Sergeant Chaney would have been addressed by his rank, "yes, sergeant", "no, sergeant", etc.
The flashback portion is set during the Korean War and revolves around a Marine unit boarding a troopship in Philadelphia to head for South Korea. Traveling by ship from Philadelphia to South Korea would be taking the long way around the planet; in actuality, US Marines at Camp Lejeune NC on the east coast traveled cross country by rail to San Diego and then shipped across the Pacific to South Korea.
When Jimmy Tully visits Nora Lee in her bedroom, she asks why he looks so upset, meaning she didn't know he was in some kind of trouble. He only says that he needs money to help somebody but never mentions what the money was for. Then she gives him her necklace, saying it should be enough to pay for the pawn bill - which Jimmy didn't tell her about.