My opinion is that Firefox’s quality is not so much an anomaly of any sort, it’s more a reflection of how stunningly neglected IE development has been. Its functionality hasn’t significantly advanced in years, simply because there’s no incentive for MS to do so. It’s ubiquitous, and most people simply can’t be bothered to find an alternative or don’t know one exists. Firefox (and Opera) succeed because they set out to fundamentally improve the browsing experience; they’ve got clearly defined goals and don’t take a “kitchen sink” approach (unlike Mozilla). These are the hallmarks of a decent software project, be it open source or not (Opera’s not). By contrast, IE is just a rectangle. It is the absolute bare minimum required for browsing the web (graphically, for all you lynx fans). You could argue that MS’s monopoly of the browser market has hurt it more than anything else, as it’s almost single-handedly responsible for their reputation for poor security (in concert with Outlook Express, that is). At a WAG I would say it’s probably the MS product that people spend most time using, and it’s truly poor. That it still holds a 94% market share says a lot about the inertia of the average computer user, though.
I’ve never been completely convinced by the argument that open source necessarily entails better security; it’s too glib to assume that a thousands of hungry programmers are scouring the open source world’s code for security flaws. Speaking as a programmer, even had I the inclination to police software in such a manner, the level of application required to bug-hunt in this manner is significantly more than most people have time for. Once publicised, holes get patches written quicker, but the task of verifying the fixes and distributing them is no simpler for an OSS project than for a traditional one. Additionally, the whole area is somewhat clouded by MS, to whom everyone looks for a comparison when considering closed source. They’ve had significant security problems, but more due to institutional attitude errors than any intrinsic property of closed source development. Most of our Windows security programs (Symantec, Zone Alarm, Sygate…) are closed source, and the world at large doesn’t tend to perceive a problem with that. I believe the procedures your development team runs, and the attitude you take to fixing problems, are far more important than the licence on your code.
Star/Open Office is another matter again, and has problems of its own that I don’t think relate to its open source nature. I think its main problem is that it attempts too much to simply re-implement Office, warts’n’all. Certainly, it needs to be inter-operable to stand a chance (my father just switched his company over to it, having got sick of the Office licence fees), but it would have been nice if it had tried to genuinely distinguish itself in some manner, rather than simply measure itself against Office as a yardstick. Of course, it’s very easy for me to say this, and developing an office suite is no mean feat. Also, I haven’t used it in a while, so my perception of it as a free-but-slightly-worse version of Office is out of date. The general approach, however, I think is still wrong. I’d like to see something attack individual Office applications, rather than attempt the whole shebang. Outlook is IMO a fairly high-quality product, and it’d take something quite nifty to get me to switch (Opera’s database-driven mail client almost managed it but was too buggy). Word, on the other hand, is a dreadful product, and is ripe for a really concerted effort to implement a better competitor. Divide and conquer, people! Are you geeks or not? 
Anyway, to answer your question; yes, you can certainly expect more from OSS, and even if you don’t use it you can expect to see benefits. I don’t believe it has any intrinsic killer advantages that will see the death of proprietary software, but I do believe that it forces proprietary developers like Microsoft to compete in areas that they would otherwise ignore. So in that way, the competition increases the quality of everyone’s software, whether you never so much as touch a Linux box.
