The number of false positives is dependant on the specificity of the PCR test, which can be as high as 100%.
I think 99.8% is readily achievable which would only give 200 false positives for every 100,000 people tested who don't have the virus.
Not to mention you should only get a test if you have symptoms and then you should be isolating anyway. The test result is merely going to determine the length of isolation.
That's 200 people who may have had a false positive test but, if they did they right thing, would not have passed on their cold or flu or temperature and headache bug, thus meaning fewer other people get symptoms that require a test.