My opinion is they are all required to be corrected.
Regardless if they are just needed for the control panel or just the forum
Otherwise you just have a forum that is crippleware.
Sooner or later you will try a feature that fails and you won't remember that you never corrected a file permission somewhere.
If you follow the documents it really is not that difficult.
Changing from windows for the first time is a little cumbersome the first time but it really is a easy task to set the permissions.
And it should take a whole 15 minutes tops.
Just follow the install docs.
Setting it to just write does not cut it.
they need to be like 777 read,write,execute.delete
or
666 read,write.
What are you using to change the file permissions?