Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
I think that sounds like erratic equipment, or perhaps a bad line or doubtfully bad power being supplied to the Polycom or the phones themselves. That's a summary of the problem makes me think of. It's no a setting problem or configuration problem of any kind.
The only other thing that might be wrong: Is your phone service digital, or analog? sometimes the difference between digital phone signals and analog phone service, on the phone line coming into your system, can cause severe problems, or even the burning out of phones. So I advise checking with your phone line service provider, as to whether they provide a digital signal, or an analog one. (What is your phone service provider?)
As for defective equipment: does the problem always happen with certain phone stations picking up on the calls coming in?
As for power problems: check whether the ground on the power to the phones, and to the Polycom, is at the same level. Also check whether surge protection is provided for the phones and esp. for the Polycom. The problem is more likely to be from difference in the voltage (or ideally, lack of it) riding on the ground, to one or more stations vs. the Polycom.
This check can be done with an electronic meter.
As for a bad line: the line in question would be the phone cords, and/or jacks. If one is shorting, or partially or erratically open, that could possibly introduce noise and the sort of problems you have mentioned. Examine phone lines and jacks, make sure none are broken, dirty, or have obvious crossing of the lines and/or the wires. This involves also examining the phone cords along their entire length for strains, cuts, severe bending, etc.
The remaining problem would be, ultimately, defective equipment, a 'broken' phone station or even the Polycom itself. That's why I advise checking all the things mentioned above.