A few random thoughts on the book::
I like Geoffery Blainey's books. I've read a few now; I like his broad sweeps, yet his ability to pick out small details.
Beyond a doubt in my mind the most influential and shaping event was communism. Even if communism didn't last, some of the ideals did. Fair working conditions, employment, a health system for those who need it, equality between sexes. The struggle with the west brought about huge jumps in technology for weapons and space exploration.
Communism birth and life was brutal. It wasn't communisms ideas which let it down; rather corruption and power of leaders. Implementation of the ideals of communism were flawed.
It would appear to me that out of the history of humanity, the 20th Century had the most going on. It certainly had the first of the 'World Wars' where death was in the millions for the combatants as well as civilians. The worlds populations have been the greatest. Technology with the birth of computers, rockets, nuclear power, planes, telecommunication. All of these have been revolutionary. I would suspect what happens afterwards will be more 'Evolutionary'.
My only criticism would be the inclusion of the New York attacks on the twin towers. I actually think that on scale of disasters be them man made or not; it was small. The American response was large; and worthwhile reporting; but both events are outside of the 20th Century.