Currently, only one user (plus the group owner and admins) can have editing privileges for a group page.
Sometimes, a page is for everyone to edit, and moving ownership around or requesting changes is tedious for the owner.
Idea: Implement the group invite system for editing permissions, in that the owner can add multiple users in the group at a time with a textbox and separated by commas, and when saved they'll be added to a list of names with checkboxes, and the owner can remove users by unchecking and saving.
Alternatively, just have a list of checkboxes for every user in the group. Whichever sounds like it makes for a cleaner UI, I guess.
I think the easier one to look at is the first one (think big groups with too many members), but might be less intuitive. Second option is there, though.