On the dozen or two occasions that i've filed a ticket, probably 1/3 of them ended up being duplicates (which i always search for, but never find, because i don't get how to use Bugzilla's search function), and another 1/3 end up going un-acknowledged. The remaining 1/3 get acknowledged, but i've yet to see one actually get fixed (which i understand is a function of resources and blah blah, i'm not bitter about it or anything).
On one occasion, i was able to locate the source of the bug i had, and, even though i had absolutely zero experience with 'lower-level' languages like C++ at the time, i decided i would fix it. I pulled trunk and managed to build it, which was an enormous affair, let me tell you, and in the end i had a fix. I submitted the patch, but was told that i would need to put it through their testing system. I was given a link to a wiki, but this entire process was just absolutely beyond me at the time and i bailed on it. I just wanted to help them fix a bug. The bug is still there to this day.
To Mozilla's credit, they did (do?) have a user-feedback extension with the beta/Aurora builds that allows regular users to report bugs in a simple manner directly from the browser. You'd pick 'Firefox made me sad' and then just type what the problem was and click submit. However, i have no idea where these bugs go, how closely they're looked at, or how successful they've been in reducing bugs.