OK, it looks like the problem has been solved. It also affected viewing Profiles which only logged in members can do.
The first thing I done was to check both the forum and server error logs which showed up nothing. I've now disabled hostname lookups in the SMF admin panel after doing a search in the SMF support forums and it appears to be OK.
(If by chance you've come across this by searching for blank screen problems with SMF, you can disable the hostname lookup by going to Admin CP -> Features and Options -> Layout and Options tab and check the box marked Disable hostname lookups).