In my case, After logging, staff members can edit/post both forum topics, one for students and another for staff member. On the other end Students can only see both topics but only post/edit students topics.
First I logged in as staff members, I can see "New Reply" and "Keep me Updated" buttons and can edit/post both the forum topics which is right according to the roles ans permission which i have set. Now I logged out, and logged in as student user, again I can see "New Reply" and "Keep me Updated" button on the forum topics related to staff, which is wrong.
Then if i clear the cache, it disappears from the staff forum topics.
So this means I have clear cache everytime I logged out from the forums.
This problem was posted as a bug some time ago by Zinn but it was closed, so I sent it again today. ( http://ez.no/community/bugs/forum_edit_button_is_cached )
I supose viewcache should be disabled with {set-block scope=global variable=cache_ttl}0{/set-block} and cache-block should be used in full/forum_topic.tpl.