Very boring support advice post
You are correct that your friends-only entries will be available to everyone you
list as a friend, and will appear on their friends pages unless you backdated
the entries, or they are viewing their friends page with a custom friends filter
that doesn't include you.
The most likely explanation for this problem is that those of your friends who
are having trouble seeing your friends-only posts are, as you surmised, not
properly logged in to LiveJournal. Since you have already tried posting a public
entry, and they were able to see that, the only further diagnostic step you
could take would be to ask them if they are able to see anyone else's
friends-only posts. If not, this provides further evidence that they are
experiencing a login problem.
Login problems are usually related to cookies, because LiveJournal uses cookies
to keep track of login information. First of all, your friends should check to
make sure that cookies are enabled in the preferences of their web browsers. If
that doesn't resolve the problem, they will need to delete the existing
LiveJournal cookies from their browsers. Instructions on how to do this are
located at:
http://www.livejournal.com/talkread.bml?journal=glitterjournal&itemid=723
Please note that this page is maintained by a fellow LiveJournal user, and is
not an official LiveJournal resource. LiveJournal is not responsible for its
content.
If you are not comfortable conveying this information to them, or if this does
not resolve the problem, please encourage them to open their own support
requests to receive personalized support on this issue.