Mistake #1- Narrowly constraining the definition of science to be what professionals do in labs, and not the basic informal inductive reasoning that people do everyday. Thereby making it seem as though people have a faith in the results of professionals in labs, and not that they value skepticism and the basic scientific method. E.G. idiocy or dishonesty.
Mistake #2- Not sure if he's responsible or someone else is, but the name of Dawkins' TV show is "The Root Of All Evil?", not "The Root Of All Evil", a title which IIRC Dawkins strongly disliked but which was forced on him, but he still managed to get a question mark added to the end.
Mistake #3- He claims that there is a kind of evidence which is not the kind of evidence involved in science, aka empirical study, aka logical positivism, aka "scientism". Of course, that's simply bullshit.
Mistake #4- He says that skepticism is self-refuting. This is the crux of the entire problem IMHO with him and most religious people. I see this argument time and time again, that it's logically inconsistent to demand justifications for claims. That overly simplified version may be inconsistent, which is why we need the more formal definitions of skepticism, which is something along the lines of "You should withhold belief in a proposition unless you have good justification for that proposition (unless that proposition is one of your starting axioms, such as this statement itself)". Of course, that will do little to satisfy these idiots. The most frustrating part is that they are skeptics, but they don't realize it. They are skeptics about most areas of their life. Maybe not well reasoned skeptics, but they apply the skeptical method to most claims. Say this, and a great many will deny it still.
I had one asshole on reasonablefaith forums who simply would not continue in conversation with me on this topic. He adamantly refused to discuss this, and continued to state that skepticism is self-refuting. He wouldn't answer the simple question (rough equivalent, I've improved since then): "Suppose we went into a grocery store, found a bag of rice that neither of us had seen before. I then claim that the bag of rice has an odd number of grains of rice. I'm *EDIT* not knowingly telling you something that is false. I have nothing to gain from lying, and I can't be lying because I don't actually know if the number of grains in the bag is odd or even. Now, we do happen to know the probability distribution is 50-50. Of my claim, do you accept it or not? If you accept it, would you also accept the second claim that the number of grains in the bag is even? Why do you not accept the claim? The only plausible reasoning I can see is that you do not accept the claim because there is insufficient justification for that claim."
Mistake #5- He wanders off to talk about secular humanism, and conflates secular humanism and science. Woh boy. One thing at a time. Yes secular humanism is a concrete belief system based on unprovable propositions, axioms, like "we ought to be decent to each other". It also happens to employ science, but humanism is not science. They are complementary, or at least consistent, and it is a total non-sequitir to this conversation.
Mistake #6- tl;dr Dakwins says that he believes that all life in the universe is the result of evolution by natural selection. The asshole makes it sound like Dawkins has this belief without a justification for that belief, that he has no evidence for that belief. He would be mistaken.
Mistake #7- He makes a lot of mentions that christians have humility, use evidence, are constantly questioning themselves, that they don't know it all, are not fundamentalists. Bullshit. Come back to me when you begin a serious inquiry as to whether you might be mistaken about whether the bible is the word of god, and when that serious inquiry involves the objective method of determining truth known as the scientific method and skepticism. (But of course, he dismisses skepticism, and we would really have to start there if we wanted to get anywhere.)
Mistake #8- Asserting without justification that the christian god exists. Gotta mention this one. Completely without evidence.
The entire video is an attack ad on skepticism, humanism, and the basic scientific method, without a shred of defense for his own propositions, just empty vague assertions that there is a god, who is the christian god, and he actually does interfere detectably in our reality. Where is your evidence?