When Jan and "Rex" are at the piano bar singing 'Roly Poly', the man behind the pianist is strumming what is clearly a four-string electric bass guitar, but the sound is from a six-string electric guitar.
When Jan and Jonathan are talking in front of the interior design store about the car he is offering her, the same extras are seen multiple times. A woman with a blue coat and gray hat walks by four times, and a woman with a red coat walks by at least three times.
A party line phone would not ring when any phone on the line was off the hook. To call the other phone on your line, you had to dial a special code and then hang up and wait for your phone to stop ringing, indicating that the other party had answered. This is not how Jan does it.
When "Rex" is split-screened with Jan when she is in bed and they are talking on the phone, you can see a fly buzzing around at the foot of it. A true high-rise apartment in the city is unlikely to have even an occasional fly.