"In 1970 the overwhelming majority of scientists believed that there was not going to be going to be global warming over the next 40 years..."
If he had bothered to do any research, rather than buying into denialist myths, he would have found that most research was pointing to warming, and that warming was a long-standing prediction of physics (see also this article).
Blainey goes on to say:
"The interesting thing to me about science is that it's given the benefit of of the doubt in ways that Christianity used to be given the benefit of the doubt."
Well, if it were true, that would because science has runs on the board in way that religion hasn't. From the eradication of small pox to landing people on the Moon, science has proved its credentials. Whenever you use your mobile phone, you are using the practical application of quantum mechanics and the theory of relativity. Religion ascribed epilepsy to demonic possession, a few Christian sects still do, with tragic consequences. But science is unravelling the causes of epilepsy and has developed effective treatments. So science has earned the benefit of doubt.
But in fact, science rarely is given the benefit of the doubt. From global warming, to tobacco and cancer, to acid rain, to heart transplants, to IVF, to the ozone hole, to collapse of fish stocks from overfishing politicians, entrenched interests and often religious leaders have fought tooth and nail against the scientific consensus, only relenting (sometimes) when scientists have been shown incontrovertibly, sometimes tragically, right. Between The Australians War on Science and members of the Catholic Church spreading misinformation on condoms and AIDS, it's obvious that science isn't being given the benefit of the doubt and is being actively opposed.
Blainey has written some wonderful history, his "Tyranny of Distance" was a seminal work of Australian history, it's a pity his comments on science are fantasy.
UPDATE: Interesting discussion in the comments thread on Deltoid's article mentioning this one.