We are having problems getting Google to index our site. We decided it was easiest to just use https for the entire site.
Do we need to change it so that the anonymous, "public", areas of the site are not encrypted for them to be indexed?
Yes, they'll index https just fine. Remember that https is a transport protocol to ensure that folks in the middle of the wire can't eavesdrop (. . . as easily . . . ) or muck w /the traffic.
They will not index password protected portions, of course.