It's starts with GUI issues where you can't resize certain things (e.g. columns in the network tab) or only in a very limited way (it got better). Not being able to inspect objects inline in the console is very annoying. Is there no "clear network log" button? No option to retain/not retain the network log on page loads? I want a way to view an element that got logged to the console in the DOM inspector (Chrome has: context menu -> show in DOM inspector). I want an auto-completion menu in the style editor in the DOM editor. And there seems to be no way to search in a script as shown in the debugger. That's such a basic function, it really makes me wonder. I want a reload menu like in Chrome, where with open inspector I can choose between "normal reload", "hard reload" and "clear cache and reload".
In Chrome's console I like that I simply can write the function name and press enter to see it's source. In Firefox I have to write "String(functionname)". That's only a minor thing. The best thing would be to get the function source expandable inline similar to what you can do with objects in Chrome's console. There should also be a link that lets you jump to the definition of the function in the JavaScript source.
There is no resource tab in Firefox. Basically I want exactly the resource tab from Chrome, with a list of all loaded images, scripts, styles etc., grouped by their origin. I want to see and be able to edit/remove all cookies, local storage, session storage etc.
You can't select a certain iframe as the context of the console, which makes it completely useless when you have to debug iframe based widgets.
I just had the case where the debugger statement starts the debugger but it did not focus on the source line where it occurs, because the debugger request the script again instead of showing the already loaded resource and the script was generated as a response to a POST request.
I don't use Firefox for debugging anymore (unless it's a Firefox specific bug I have to fix) so I don't quite remember the next bit: There where some kind of big annoyances concerning debugging and exceptions which are caught anyway. I could not get it to "halt on exception" but not on those that are caught.
That's all I can think of right now, but I'm sure I forgot something.
But granted, it is always getting better. Maybe some day it is as good as the Chrome Inspector. There is one point where it (or Firefox) is better: Error messages. They are much less cryptic and show the source line of the error. It says things along the lines of "in foo.bar foo has no method bar" instead of "undefined is not a function". Also a rethrown exception retains the original source line, which is very useful.
Firefox's font inspector is nice. I hadn't had a use for it yet, but I can imagine to have one some day.
In course of writing this comment I looked at the Firefox development tools again and a lot of things got indeed much better since the last time I looked.
OT: There are also a lot of things that annoy me about Chrome: Since many month now Linux integration got extremely worse. They dropped gtk for their own thing and screwed up big time in doing so. Context menus look totally alien and have no shadow, tooltips (title attribute) look alien and are no real windows (they get cropped, which makes them useless in certain contexts), there are lots of graphical glitches, e.g. when dragging stuff (white bg of the dragged image/text and for the drop marker arrow in the tab bar) and the scrollbars got the brain dead Windows behavior that not even IE uses anymore. IE implemented it's own scrollbars, apparently. Other scrollbars in Windows (and in Chrome) jump around and stop working when you drag the scrollbar and move the mouse an unknown invisible distance from the scrollbar. Oh and dragging tabs got unusable bad in Chrome. It's a complete disaster. The tabs aren't transparent but full sized when you drag them and you can't drag them down so the bottom border of the window gets outside of the screen, which makes it impossible to drag a tab to a different window that is located down in relation to the window you ripped the tab out of. And sometimes tabs move at an offset form where you grabbed them. WTF? There was a time where Chrome looked less of an alien under Linux than Firefox. Not anymore. Firefox didn't get any better, Chrome got much worse. At least you can use the mouse wheel on the tabs. That is something it does better than Firefox. And the tab size handling when closing tabs one after another. But enough of that.