Towards the end he shows a lack of understanding of statistics. He claims if any infinitesmally small change to the laws of nature would have caused an uninhabitable universe then it must have been specifically designed the way it is. He brings several examples that actually are all the exact same argument.
The mistake here is that he assumes that there was only one random try at creating this universe and that we cannot have been sooo extremely lucky. There is no reason to believe that there was only one try. What if there were a large number of tries? If all the other tries resulted in uninhabitable universes then of course us being in the lucky version must make us think this was not random chance.
Example: ask a large number of people to flip a coin ten times. Eventually you will reach someone that actually flipped ten times heads in succession. What would that guy think? Clearly that's not a normal coin and you designed the whole thing to be like that because what are the odds of him flipping ten times heads? He does not know about the other thousand people you had play this game that didn't get ten times heads.