I'm on the release update channel on most of my systems, so primarily using Firefox 13 right now, but this has been a problem since forever.
As for the rest, I'm sorry but I'm rather unforgiving of the extension buck-passing dance these days. It may well be that this particular problem is caused by an extension, and no doubt if I went through the usual production of disabling things one by one, running safe mode, messing around with config pages and all that jazz, I could probably pin it down. But the bottom line is that it should not be possible for any extension to cause severe performance, reliability or security problems. If that can happen at all, then Firefox is demonstrably broken on an architectural level, and it really is as simple as that.
(Lest you think I'm being flippant: one of my many hats is "professional web guy", so I do have a whole bunch of test systems and I do use use every major browser regularly. I don't tend to criticise browsers on technical grounds unless I have either a reproducible bug or a repeated pattern of poor behaviour across multiple systems and an extended period of time. This is the latter.)
The Firefox extension system is extremely powerful, i.e. extensions operate at the essentially the same level as the original browser code, which allows for really useful extensions which can only work effectively at that level. Obviously this means that code in extensions can "break" Firefox just as much as code in the browser proper.
Configurability like this is always a trade-off between power/efficiency and safety/reliability: if you want to allow others to fundamentally extend your product so that the extension is efficient/fast, you're going to need to give them deep access. Firefox has chosen to be more to this side of the spectrum, Chrome/Opera/IE have chosen to be more towards the other.
So the extension "buck-passing" is valid: you should be complaining to the extension author who has a memory leak, or who is running an infinite loop (or whatever). After all, you didn't have to install it.
(That said, Mozilla has recently been putting significant amounts of effort into making it harder for extensions to be "bad".)
I do understand the choice Mozilla had to make between control/sandboxing and power/flexibility. I just think that, with the infinite wisdom of hindsight and a view from the cheap seats, it was the wrong choice, and now they're paying the price.
It is unfair to blame Mozilla for the resulting problems, just as it's unfair to blame Microsoft because someone wrote a virus that infects Windows machines. Unfortunately, as in that other case, the value of the platform would be extremely limited without the extra functionality built on top. Put another way, I don't have to install the few extensions I use, but Firefox would not be worth using anyway if I didn't have them. The bottom line is that the platform is part of what you experience as a user and the platform's weaknesses can undermine everything running on it.
That all said, it is also fair to say that Firefox has had its share of performance and reliability problems without any help from extensions, and the architectural limitations in terms of tabbed browsing are well known. It may be that the poor behaviour I've observed recently has been caused by extensions, but it may not. To be blunt, it's not realistic for the Firefox developers to expect your average end user to go through an extensive process of systematically testing their combination of extensions and all the other fun and games every time the performance drops. Most people simply aren't going to do that, and they're going to point at Firefox and say "Well, Chrome gets it right" or something instead. It's not fair, but you've got to play by the rules of the game.
(I don't get the UI stalling for very long ever, and I have tens and tens of tabs open always.)