PSA can definitely give false positives, but that's better than false negatives! I think they know how to interpret PSA results fairly well these days, and generally speaking they aren't too worried about the actual figures, as long as they aren't astronomically high, rather the trend over several months. My PSA was monitored for about 9 months or so and kept rising, which is why they investigated further and found cancer.
It's an imperfect test, but I'd still recommend anybody over the age of 50 to get it done regularly.