@JohnZ
You are right; I would not claim that the inaccuracy in the genealogies reduced the authority of Scripture. But the people I have read who spend time trying to harmonize the genealogies do not seem to be doing it merely for apologetic purposes, i.e., to prevent doubt arising about the authority of Scripture. They appear to personally believe that not a single iota in either genealogy is wrong and that both genealogies are correct and without error, and that the discrepancies are only apparent, and that a little thought, maybe a little research on the time period, etc. will eventually remove the discrepancies. I would disagree. I have seen just about every variation on how to reconcile the genealogies, and they all smell like the proverbial something rotten in Denmark; all seem like ad hoc special pleading to “rescue” the text from the charge of falsehood. At most only one of the genealogies could be correct, and I doubt that either one is; further, I doubt that either one was even intended to be the product of genealogical research. And that’s exactly how I think about the Flood story, which is why I made a comparison between the two.
Nobody’s faith should rest on the accuracy of the genealogies of Jesus, and nobody’s faith should rest on the historicity of the Flood story. If I meet someone whose faith does rest on those things, I make an assessment before speaking to the person. I ask myself: “Is this person a simple believer, a good person, but one not much given to reasoning, a person for whom challenging the literalness of these stories might harm his or her faith?” And if the answer in my mind is “Yes”, then I change the topic to the weather or sports; I’m not in the business of using my scholarly knowledge to pass on “enlightenment” that will destroy simple people’s faith. But I also ask myself: "Is this person a swaggering amateur theologian, or even professional theologian, who is putting his chin out, and saying “I double dare ya,” declaring that he can prove the Flood happened, or prove that there are no contradictions in the genealogy of Jesus? If the answer to that in my mind is “Yes,” then I will dismantle this person’s certainties, in an attempt to leave him in a state of intellectual crisis, not about faith, but about his particular literalist-historical hermeneutic; he needs to come to see that his Biblical hermeneutic is shallow and he needs to think more deeply about what the Bible is, and what Christianity is; and if my intervention causes him to lose his faith, well, then his faith was never worth having in the first place. He should have based it on the core affirmations of Christian faith, not on mechanical trivia.
You have not correctly assessed what Dawkins’s reaction to me would be. He would be perplexed, unsure how to respond, because he would expect that I would defend a literal global Flood. All his arguments at the ready would thus be useless, because I had immediately ceded his point. Now he would have to figure out where I was coming from, and that would knock him off his game. His tactics work best against literalists; they roll off the back of non-literalists like water off a duck. Instead of spouting his usual “shpiel” he would have to converse with me, find out what I mean and what I think. With Ken Ham, he doesn’t have to do that. He knows exactly what Ham believes, and knows exactly what weapons to deploy to show that Ham’s position is unsustainable. In my case, he’d be tongue-tied and stammering and flustered. Literalists are actually the greatest Christmas gift New Atheists could possibly have. A hunter loves it when the deer or moose walks out into the clearing and stands in his sights. But when what he thought was a deer turns out to be an armadillo, he isn’t sure what to do.
As long as there are literalists, there will be militant, anti-Biblical atheists; and as long as there are militant, anti-Christian atheists, there will be literalists. The two feed off each other. But their battles mislead the public about what is important in religion.
As for your final question, I think that the right position for a traditional Christian to take is that Scripture is true “in all that it teaches”; the problem is that we do not agree on what it “teaches”. You think it “teaches” that there was a global Flood in 2340 B.C. I think it “teaches” no such thing, but offers a moral tale which makes use of standard ANE legendary and mythical motifs and puts them into the context of Israelite religion. Therefore, even if there was never even a local Flood, let alone a global one, I don’t think Genesis has “taught” anything that is false. There might well have been a local Flood in the ANE at one time, and there might even have been a global Flood thousands or millions of years earlier than the Biblical genealogies indicate. But the historicity of the Flood is incidental to the meaning of the story. That is not the case in all Biblical stories. So each one has to be taken on a case-by-case basis. The question must always be, not “What does this story say?” but “What does this story teach?” It is characteristic of literalism to make the two answers the same in almost every instance; non-literalists more often see the two answers as different.