There were no portable battery operated broadcast quality open reel tape recorders in the 1950s.
The shiny tip-ring part of cable ends should look clean and bright, thanks to the friction of being used over and over. Also, an operator wouldn't be touching the connectors, due to dirt and finger oils. Between the corroded ends and the way she was touching them, of course she was hearing strange sounds on the line...
The character Fay wears glasses of a style that didn't exist in 1958. The shape is cat's-eye but the lenses are too big and the frame color is wrong for women's frames of the era.
At the 25:50 time mark, during the "switchboard" scene when Fay says "We're having a lot of switchboard ISSUES tonight.", it is MUCH MORE likely that in the 1950's she would have said "We're having a lot of switchboard PROBLEMS tonight.". The word ISSUES didn't really become a replacement for PROBLEMS until about the mid-1980's with the advent of "politically correct" corporate-speak.
The black telephone in the radio studio has a white modular plug-in handset cable that is incorrect for the period. It would be very unusual for the handset cable to be of a different color from the phone, because at that time the cable was permanently connected to the handset and receiver and could not be unplugged and switched out by the user.
The radio station apparently played a 45 RPM single record for the whole time the two characters left it. When they return, there is no audio of it scratchily playing, and Everett doesn't monitor it in any way on headphones, and then Everett talks on the phone for quite some time before turning off the record and going on the air; of course, no 45 record would have lasted that long (unless it had been skipping).
Whilst it's strictly true that geographically the radio station would begin with a 'K' - as it's a fictional station the WOTW station is undoubtedly a homage to the best radio/aliens show ever produced.....War Of The Worlds.