During Eddie's recording session, his song is being recorded not only on tape (correct for 1960) but directly to a master disc. Record companies no longer recorded directly to master discs after tape was introduced in the late 1940's and became the standard way of recording in the 1950's.
When Eddy and Helen are out shopping for new clothes, they stop by a bar for a drink. When they approach the door Helen gushes about how good the food is there but her lips only move for the first line of here speech.
When the record producer calls in to his secretary, we see a shot of a woman sitting working a switch board, she tells the producer that the switchboard is lit up with calls regarding Eddy's first TV performance but she is clearly not speaking those words.
The Ford sedan driven by Iris changes back and forth between a 1949 (plain horizontal bar grille) and the equivalent 1950 model (with a round feature in the grille center). The '49's damaged trunk - dented in on the passenger side - also comes and goes in various shots.
When the gang drops by Nadine's diner after the opening heist, the shadow of the boom mic is quite visible in the top left-hand corner as it passes over Nadine's face. More crewmembers' shadows are seen on the door in the back of the shot for the first 20 seconds or so of the scene.
When Eddy asks Mooney to leave the hotel room so he can talk with his agent, Mooney walks out of the shot and we hear the hotel door close. Mooney's shadow, however, can still be seen on the wall, revealing the actor is still on the set.