Right now this is very obvious with the tools menu. If you assign a user a maintenance_mode capability it can not access the relevant page since the menu related code generates a "Sorry, you are not allowed to access this page." message
going to punt the core problem to later and just fix tools menu for now by introducing a special capability to control the tools menu and add a filter to calculate it base on the capabilities of the sub menus.
Right now this is very obvious with the tools menu. If you assign a user a maintenance_mode capability it can not access the relevant page since the menu related code generates a "Sorry, you are not allowed to access this page." message