Aside from the age old privacy issue (cookies, referer data, etc.), I am unaware of any problems with Mozilla. Does that mean there aren't any? Of course not.
There is a lot of animosity towards Microsoft and their products. There is also a lot more genuine scrutiny and hysterial media attention because of the wide spread use of Windows. All ot this means two things: people are more likely to look for problems and more people are going to talk about those problems.
Now I'm sure you can claim that an unknown vulnerability is not a vulnerability because nobody is able to exploit it. On the other hand, I would suggest it is just as much of a problem — particularly for businesses and governments who may be targetted for proprietary information. Fortunately, most of us aren't considered to be all that important so no one will invest that sort of time/money/expertise into exploting the problem, but it still leave an opportunity for the vulberabilities to be discovered and later communicated.