I think that one way in which Russell's essay can be analyzed is to determine his starting point and his philosophical frame of reference. A reason as to why Russell is such an intricate and unique thinker is in how he challenged both sides of the political spectrum. He was not Marxist and he was not a nationalist. He was not a utilitarian and was not wedded to any particular dogmatic notion of understanding. I think that analyzing the essay in terms of what Russell rejects might be one approach to take because it reveals the complexity of his thought. Such an approach also details the challenging position he took in the face of so much opposition.
Another approach is to examine how Russell takes ideas that have not helped mankind to their logical consequences. His critique of science as providing the ultimate answer is a part of this. A similar tenet can be seen in how Russell criticizes those who believe the idea of a soul has helped mankind. Russell's writing suggests that the embrace of technical ideas might not be as beneficially as the moral ones. For Russell, moral ideas are the ones that help mankind because they help to guide the technical notions of consciousness: "...the present state of the world and the fear of an atomic war show that scientific progress without a corresponding moral and political progress may only increase the magnitude of the disaster that misdirected skill may bring about." Analyzing how Russell is able to merge philosophical analysis with a pragmatic sensibility helps hin being able to take inquiry to its logical conclusion, how it has played out in historical consciousness. This might be another approach to take when analyzing the value and merit of his essay.