I really like Firefox, apart from it being a really memory hungry beast it's almost perfect with everything that it does...but the documentation of Fx is something which I would say is far from being comprehensive so mostly you have to find stuff on your own. few things that I've found are:
a) Many a times you want to search using the search box without leaving the current page, well go to search box (ctrl-k), type in your query and hit Alt-Enter & viola the results open in a new tab. You can also pick the search engine by using the keyboard (press Ctrl-Down/Up Arrow key). There are tons of search engines to choose from in case you are not satisfied, try http://mycroft.mozdev.org.
b) How do you open a Url on a page if it is not hyperlinked for e.g. the mycroft link above, you don't have to copy the Url, open a new tab & paste the link, just select the link with the mouse and drag it to the tab-bar or to one of the opened tab.
c) File-Exit, is different from Alt-F4 or Close Window. It exits Firefox completely including all open Fx windows (download manager, other Fx open windows included).
d) How many times you would wish that Fx would automatically authenticate you against a given server much like the way IE does? Don't fret there is way for that too, in the location bar type in about:config , in the filters type ntlm and dbl click network.automatic-ntlm-auth.trusted-uris, type in the name of servers for which you want to be automatically authenticated separated by comma and you're done.