Policemen will generaly reduce corruption and waste by one gold and one shield, respectively -- this shield and gold then gets the benefits of any improvements the city has (i.e., an extra gold might equal two gold after the effects of a masrket and bank in the city, depending on slider settings). But, the policeman may also have no net effect if the city is well over the 100% corruption limit, meaning the policeman would do nothing.
Taxmen give 2 gold to taxes (not subject to city improvements) regardless of the city's degree of corruption. Scientists give 3 science beakers (not subject to city improvements), regardless of city corruption. Civil engineers give 2 shields (not subject to city improvements), regardless of city corruption, but only work for city improvements (not units).
And I second Fanny Brice's opinion -- the improved classic specialists and the new specialists can be powerful (I find the policeman less so than the taxman, scientist, or CE, but still useful in certain cities).