I completely agree with halirutan about the worth of a bug tracker system for Mathematica, it is something very useful for developers like us, which spend almost every day on Mathematica.
In my experience (about 20 years) of Mathematica's evangelism, I met very few people which were negatively influenced by bugs. Generally speaking, who works with software knows that all software, really all, has some kind of bug or wrong behavior. Moreover, consider that if you are going to make an investment on a software, in terms of know-how more than on the licenses, you should be aware of any problem influencing the area of application you intend to use the software for. On the other hand, even if you know there is a bug in a specific context you will never use, this will not influence your decision. So, in any case the makers of that software should be happy of that, because you can decide without being fooled by the limited information about their product. In other terms, a serious tracker system can help people who already works with Mathematica and help other to decide if the software is suitable or not for them.
Of course, stupid people will always speak against the software or the company (Wolfram), starting from a bug or even from a negative comment here on SE, this is inevitable with or without the bug tracker system.
What I would suggest is to use the same professionality used here on SE, that means trying to keep a good and serious level of comments and try to be focused on the actual problem and avoid unuseful comments about why a bug is there or why Wolfram doesn't remove that bug. We cannot know how complex is the internal process of a software house producing a huge software like Mathematica, so there could be thousands of reasons why a bug is not fixed when we wish.
On the other hand, the tracker system will save a lots of our time, allowing us to be aware of a bug and avoid to spend time trying the correction of something wrong that doesn't depends upon our code. Finally, another positive aspect is that with the contribution of the SE community, a bug can be easily overcome by workarounds suggested by expert users, so even beginners will take advantage, also appreciating the versatility of Mathematica, that allows many different ways to obtain the same result.
Finally, another possibility could be to create something with limited access only to those having a good reputation as SE users, so to limit the possibility of a misuse of the bug's list and related comments. Personally, I don't like closed groups, but considering we are discussing critical aspects of a commercial software, this could be a sort of compromise to show our professional intention to contribute to the software development and to its adoption and not to damage it or the its makers. Not sure this is possible, but could be a starting point.