People are watching The Ladykillers, which came out in 1955. When Geordie and Will are looking through a character's house, thought to be an American, there is an American flag with 50 states on it. In 1955, there were only 48 states (Hawaii and Alaska didn't get statehood till 1959) but the flag had 50 stars on it.
The medal held up by Geordie was the Distinguished Conduct Medal ("DCM"). He authoritatively described it as the Distinguished Service Medal.
There Distinguished Service Medal had a different, largely light blue, ribbon and was awarded to members of the Royal Navy and similar.
The DCM was awarded to the 'ranks' and was similar, though lower status, to the Distinguished Service Order ("DSO") - which has similar colours in its ribbon but which takes the form of a cross. The DSO was award to officers.
Tom Morley's character was listed in the closing credits as Edwin Hensler, but the only time his name was used in dialogue, it was Edwin Parker.
At the crime scene, Geordie picks up a bloodied glass ashtray that is apparently the murder weapon with his bare hand. Even in the 1950s, cops knew about fingerprints and a smart veteran like him would have used some sort of cloth to lift it rather than spoil potentially valuable evidence of whodunnit.