Mechanical collection followed by manual inspection, often through a microscope. This being HN, "a prime candidate for disruption via cloud-based deep learning methods." ;)
Mold testing is hard to research because there are no standards. As http://www.ianrpubs.unl.edu/pages/publicationD.jsp?publicati... comments, "http://www.ianrpubs.unl.edu/pages/publicationD.jsp?publicati...
http://home.howstuffworks.com/home-improvement/household-saf... goes on to say that "Consumer Reports conducted an evaluation of home mold testing kits in 2006, and none of the four kits they looked at received a recommendation. The problems ranged from the kits having no expiration dates, potentially compromising the results, to being difficult to use"
One solution seems to be to lead the mold spores land on a Petri dish, incubate the dish, and inspect to see what grows. The non-professional solution is to use one's nose to check if anything smells moldy.
Pollen count is also done by manual inspection, in this case by inspection of the pollen grains. See http://www.wral.com/weather/blogpost/1389497/ . At http://www.aaaai.org/global/nab-pollen-counts/counting-stati... you can see how people get certified to be a pollen counter: "A counter will receive a pollen slide with instruction sheet. The slide and completed score sheet is returned to the NAB and graded. Pollen certification will be given if the pollen grains have been counted correctly."
It then goes on with mold counter: "A counter will receive a mold slide with instruction sheet. The slide and completed score sheet is returned to the NAB and graded. Mold certification will be given if the spores have been counted correctly."