I use PrimeFacesMobile 6.0 and when I have a p:calendar and below one or more other components like p:selectOneMenu/button/text, the mobile browser doesn't work with p:calendar days, it clicks the p:selectOneMenu that is below, it only works if the day is "lucky" and positioned in a region out of all the other components in the page.
I tested the calendar from RichFaces, and it works fine. The problem is that RichFaces doesn't have mobile support like PrimeFaces.
I think there is some problem with the panel opened by calendar to show the days.