Thank you for your thoughtful response.
I think I should start with an apology to the Chrome team, because I realised after posting that I was actually thinking of the Chromium issue tracker and its Bugzilla counterpart, not the Chrome reporting mechanism under "Tools" and then "Report an issue...". The latter actually seems to be a very good starting point for reporting a problem.
Regarding the more challenging bug trackers, I think it might be instructive to consider those systems in the same light we would consider the kinds of web start-up we often discuss here on HN. We talk about having clear calls to action, and not forcing someone to sign up with their e-mail address before they can even see what they're getting themselves into, and the psychology of giving users clear choices and avoiding analysis paralysis. This is all good stuff, and it's just as applicable to writing a user-friendly bug reporting system as any other web app.
Take a look at https://bugzilla.mozilla.org, which is the top hit for the search term "Report a Firefox bug". On that page, there are four big options, any of which might be what I should do first if I want to help. There's also a text box, which has a label similar to one of the big options, a bunch of separate related links next to that box that again seem to overlap with the big buttons and additionally suggest that I might need some sort of plug-in to do something. There's another search box in the menu across the top of the screen, along with about 10 other links. There's another row of links below all of that lot.
Now go and look at http://www.google.com, which is what I used to find that page. Except that I didn't really even do that, because the one relevant box was right there in my browser already.
Suppose I don't immediately give up, and I decide that "File a bug" is the most promising option on the Bugzilla page. Clicking through there, it seems that before I can find out whether I'm in the right place, I need to deal with a page prompting me to log in. At least, I think I need to log in, because there are form fields that look like I should on top of the 4 other text boxes, 4 buttons that look like buttons, 1 other button that doesn't look like a button, 2 checkboxes, and 20 links also on the page. However, as a new user, what I actually need is to create an account, which is accessible via a link set in tiny, low contrast text in the small print several lines below the login form.
OK, so I've spotted that link, and I click through to create an account. The next page does have a lot of nice, large, clear text. In fact, it has a whole load of links that I can use if I need help on one side of the page and a load of things for me to read on the other side. This is a classic analysis paralysis situation: if I'm here to file a bug, do I want help or am I trying to help? At the bottom of the right-hand column is, in smaller text, a place I can put in my e-mail address to create an account, under scary-sounding wording about alternative e-mail addresses (which have something funny about them that I need to follow a link to understand, apparently) and about confirming things work before I can get on with doing anything useful.
At the bottom of the left-hand column of that page, under the generic heading "Feedback", is what actually might be the most promising link: if you click that and then click "Firefox makes me sad", and you ignore repeated attempts to divert you elsewhere, you get to what seems a useful page: a box to type in a problem and a place to add a link to the page where it happened.
Obviously I'm deliberately describing the system critically here, and I'm picking on Mozilla rather unfairly since Bugzilla is hardly the only bug tracker with usability problems. However, I hope that by being specific, I am making the point about how difficult it would really be for an average user to report a problem. I've taken more than half an hour to write this message, looking through numerous pages on Bugzilla to get this far as if I were a new user, and I haven't even got to the main bug reporting page yet.
Just to finish the story, the actual page itself has far too many options for any non-expert user to be confident with it as well, even for professional web developers who use the system somewhat frequently, but this doesn't matter all that much if most people never get that far anyway.
Perhaps the most unfortunate thing of all is that despite being willing to help, the first time I ever said all of that was in response to an HN post where someone seemed genuinely interested in why I thought there was a problem. I honestly wouldn't know where else to send it, or whether someone somewhere might care enough to do something about it if they knew. Maybe if it's here it'll filter back in some useful way at least.