It is stated that the record on the turntable was still playing when the body was discovered. This would not have happened because the turntable is a 'record changer' that automatically shuts off when the control arm is engaged and there are no more records in the stack. In the flashback sequence, Harry Prebble is shown activating the control arm. If it had been left disengaged (up and to the side) it would have played the record continuously as mentioned.
At the end of Nora's first visit with Mayo at Bill's Cafe, when they are leaving, he is held up by some friends just coming in. She hustles out and gets into a cab of early '50s Chrysler Corporation manufacture (looks like a '52 Plymouth). When Mayo frees himself from his friends and rushes outside, he sees what is apparently meant to be her cab rounding a corner at the end of the block. This time it's archive footage showing a Chrysler product of the late '40s ('47 Desoto, one would guess). DeSotos were very popular as cabs in post-WWII days because they were as large as Chryslers, but at the next lower price range; in the early 1950s, smaller, lower priced Plymouths were more frequently used.