They will fear and defend against anything that question their belief system. To me it's simple: Why do you need this belief system? (not how you'd approach it, but just the gist of what you'd ask) This works on a deeper level because the basic reason why JWs and so many other people with religion is because it's a kind of security blanket, the specific contents of the belief system is not that important. If you want them to open up without being defensive or feeling threatened, offer them something that will free them from that fear. So I wouldn't so much point out a flaw in the bible, but point to something from the bible that indicates they don't need this crutch. If you take a step back and look at the typical mind set of JWs, you know the bible is going to be a biggy, it doesn't make a lot of sense to try to take on the bible atleast as a first step. Just turn it around. Go with the teachings that basically amounts to "all you need is love" - the good samaritan, etc. You say you don't want to beat up on them, so offer them support instead. Use something that's already within their belief system, strengthen that so they can overturn the other parts of their belief system.
One thing to keep in mind is the witnesses come to your door with an agenda - any results you're going to get is dependent on whether they're willing to put that aside and actually openly discuss with you. If they're not, I am not really interested in getting them to stop being a witness. The thing is, with a certain attitude it is irrelevant if they are witnesses or belong to some other religious group, so details about doctrine is really meaningless to me at that point. If they are so puffed up as to be beyond reason, maybe they need to crash in order to wake up. But on the other hand, if they are already kind of tired and actually WANT to leave on some level, you supporting them as a fellow human being can make all the difference. What I propose is that you work some biblical stuff in with that support so they can connect with you. You don't have to believe the rest of the bible, just use that as a language in which to communicate with them.