If you do want to enable parts of Firebug globally, you can do this:
Click on the tab you want to enable, the main firebug window will give you the option to enable bit for just this site, and a 'down arrow' icon will appear next to the tab.
The down arrow will give you a menu to set its enabled/disabled state.
By default it is disabled for console, net etc.
The options this menu gives you are to have the tab enabled/disabled just for this site, and enabled/disabled for ALL sites (except for those where you have already set a per-site option).
Select enable here, and this tab will be globally enabled. All future sites you visit will have this tab enabled without you having to go through these steps.
If you do this for each tab, it'll be enabled for all the tabs, all the time (again, apart from any sites you choose to have per-site settings for)
The trouble with having it turned on all the time, is that some sites will use javascript to continuously poll the server via AJAX. For each of these requests, Firebug dutifully stores the request and response in a list.
If you spend any time on a site like that (Gmail, for example), that list grows to such an extent that the whole of Firefox starts to become slow and unresponsive.
I think Gmail now issues a specific warning if Firebug is active, but other sites may not.