I like the 'suggested edits' feature but I don't like how it appears on SO. If there is a suggested edit the content of the toolbar gets shifted left to make room for the number. I find this distracting; I prefer the toolbar to never shift around (unless I'm getting rep/badges, of course).
I say remove the notification from the toolbar and move it to the tools screen, in a new tab called 'edits.' Obviously the tools page would have to be made available to users who wouldn't normally have access to it, but the tabs that support features they don't have access to can be hidden.
If the notification must be in the toolbar, create a fixed width space for it and for god's sake don't give it that reddish orange background. I think this number (with its red-orange background color) stands out too much for what I think feature that belongs in tools.