Although I knew from the title that I probably wouldn't agree with a lot of this, I found it a very enjoyable read. It includes essays of varying lengths (the shortest is less than two pages, the longest 27), on the existence of God and ethical questions in general. On the more general questions, Russell is definitely a liberal, opposed to forced conformity and social hypocrisy, and his views are pretty close to mine. I particularly enjoyed a couple of historical pieces - a review of two books on medieval history and a sketch of the life of Thomas Paine.
On the existence of God, the most interesting of several pieces is a transcript of a radio debate between Russell and a Jesuit, where Russell clearly wins the argument about logical proofs, doesn't make as convincing a case on ethics, and has no answer to the question of religious experience. (The Jesuit misses a chance to push Russell on what I have always seen as the weakest point of his side of the argument, that science and logic are not in fact able to explain the whole of human experience; and the anti-God response tends to be to pretend that things which don't fall into the domain of science and logic don't need to be explained, which is then a tautology.)
I still prefer Russell's approach to that of, say, Richard Dawkins, because Russell seems to me to have a better grip of the problem: he quite rightly attacks dogmatic beliefs, be they Christian or Communist, held tyrannously by anyone, and advocates free thinking and debate; and one of his arguments against religion, in particular Christianity, is that it usually fosters and leads to this sort of tyranny. My own view is that it is a categorical error to blame this pattern of human behaviour, which is found and has been found among rulers of all religious backgrounds and of none, on religion per se. (There are also plenty of examples of states with a strong religious consciousness which none the less practice or practiced pluralism, but Russell discounts them as not being religious enough, which by his lights they aren't.)
The book finishes with a long (40 pages) description by the editor, Paul Edwards, of an incident where Russell was barred from taking up a professorship at the City College of New York as a result of an outrageous court judgement, combined with political machinations by (ultimately) Mayor LaGuardia. It is a depressing story, and illustrates that the American system is not always all that it is cracked up to be; but this is perhaps less newsworthy in 2008 than it was in 1940.