Very often, I get asked about the reliability of open source, and have wondered what is the best analogy to explain it. I had an epiphany the other day - medical science.
When we are ill we go to the doctor, who makes a prescription. And when we hold a pill and a glass of water in our hand, on what basis do we have the confidence that this pill will cure us, or at least that it won't kill us? After all we haven't personally verified it, have we?
It is on the basis of the transparency in the process of developing it. This includes basic research, publications, open peer review, criticism, field trials on animals, government approvals, human trials, well defined standards in the manufacturing process, etc.
Likewise, the open source software development process provides transparency. You may not be able to personally verify the source code for the product you are using, but if it is popular enough you can be assured that it has been seen by developers and other experts around the world, and unless there was a global conspiracy involving all of them, the product you are using is reliable.