PCR is, as Yeadon say, an amplification technique. An unfortunate downside of which is that the protein used to generate the new strands of DNA/RNA are polymerases which possess no 'proofreading' mechanism.
The principal of the PCR test is as follows. We add patient's sample, lots of materials and a 'builder' (polymerase). The builder identifies that he need to make a load of fences the same as the ones he's seeing in the sample and so he gets to work. There are materials called primers which help with identifying which fences he needs to make copies of. Problem is this builder's been going at it ten to the dozen and by the time he's made lots and lots of fences there's a chance he's starting to make mistakes. He's so focused on the job he doesn't realise the mistakes and there's no foreman to check the quality of his work.
Okay this is a crude and silly example but in principal, PCR is absolutely specific as a technique, to the same point as any other test we have for any other disease. The primers we design are based on bioinformatics work to identify unique regions of the virus's genetic code and this part ain't easy. We do the best we can as scientists, we don't have instruments where we put in the sample and get an unequivocal result every time. There are things we can do to control these replication issues such as limiting the number of copies we make. Yeadon talks about 2^40 copies and I just about laughed. I haven't done PCR for about 10 years but I'm not sure any scientist would go beyond 2^30-35 - at which point you've already made >1B copies of the original RNA/DNA and are well into detectable territory.
You know when you watch crime shows and they say the DNA matched with a certainty greater than the entire human population to have ever lived? They are using PCR to determine that.
