The Argument from Design is a variant of the Natural Law argument. It states that everything in the world is made just so that we can manage to live in the world.
Russell argues, on the basis of the work of Darwin, that the reason why living creatures are well-adapted to their environment is because they grew suitable to it on the basis of adaptation. So, ``there is no evidence of design about it''.
The rest of his argument revolves around his subjective view of the world, for he conjectures that if people had omniscience, omnipotence and millions of years at their hands they could create better things than Ku-Klux-Klan or the Fascists. Moreover, according to the ordinary laws of science one has to suppose that the life on this planet will die out anyway. To counter the charge that such a view is depressing, Russell argues that no one is worried about what will happen to the world millions of years hence.
They are worried about something much more mundane, or it may merely be a bad digestion; ... Therefore, although it is of course a gloomy view to suppose that life will die out - at least I suppose we may say so, although sometimes when I contemplate the things that people do with their lives I think it is almost a consolation - it is not such as to render life miserable.
It is true that Darwin's research has indicated a mechanism whereby organisms adapt to their environments, i.e evolution. However, it says nothing about why this mechanism is there? Moreover, Darwin's research gives no insight into how exactly does this mechanism work. The experimental evidence for evolution rests mainly on simple single or multi-celled life-forms that reproduce quickly or on studies of skeletons and fossils of the life-forms of the past geological time periods. Moreover, one can always argue that the process of evolution in itself is an evidence of design since it empowers life-forms to keep in pace with their environment.
His argument that if God had really designed people then there would have been no place for people like the Fascists can be worded in the following way: ``Should God create the best?'' This question had been posed and answered centuries before Russell, amongst others by Liebnitz. God need not create only the best that is conceivable, it might be optimal for the world to have a tousle between justice and injustice. Moreover, if a person with his or her free will chooses to do something that is not commensurate with his or her abilities, then how can one blame God for the person's decisions? Even more so, Russell's view of Evil as exemplified by the Fascists is a very naive view. The enemies of the Fascists, the British, were not angels themselves. The books of history are a record to their cruelty and exploitation.
His last comments actually trivialize humans and take a very arrogant point of view that only Russell can see correctly and all the others are misguided. I will not comment on his closing statements.
The argument itself is weak, however, Russell's criticism of the argument does not stand upto scrutiny itself.