Isn't it better to map these three town squares (Piazza della Cisterna, Piazza Duomo, Piazza delle Erbe) as highway=pedestrian+area=yes instead of place=square? Can't find an answer in OSM-wiki, what differences apply here.

The streets crossing the squares don't have street names, which causes bugs in quality tools like OSMOSE (address with no  corresponding street in proximity). Perhaps mapping the nameless street segments as "Piazza della Cisterna" can solve this problem.