When harry hands Norah a glass of champagne, she takes it in her left hand while holding her purse down by her side with her right hand. But, in the next shot, her purse is suddenly over her left arm and she is still holding the glass in her left hand.
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 1950s Chrysler Corporation manufacture (looks like a 1952 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 1940s (1947 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.
The "champagne" that Norah drinks before she reads her fiancé's letter isn't carbonated.
Perhaps unaware that his hands on the keyboard are visible in the mirror behind him, Nat 'King' Cole plays a strikingly different piano arrangement of "Blue Gardenia" than the one heard.
The name for Greyhound buses was first used in 1929. Mayo said he was born on a Greyhound bus which would make him 24 at the oldest. He looks much older.