The idea of the Doomsday clock being closer than the cold war is silly.
Considering that the doomsday didn't eventuate during the cold war then it is not necessarily wrong to say that it was closer then than now. The main difference between the danger being face now and then was that back then you didn't have a huge segment of the population disbelieving the experts who said that the world was in danger. Nobody was so stupid enough to say that just because people died before the atom bomb was invented that it means that bomb couldn't be responsible for killing anyone now (to adopt one of the anti-AGW lines).
We are actually closer to danger now because politically we are further from a solution than we were back then. At least both sides recognised that they had to consider the ramifications of their actions and that something had to be done. Fast forward to today, and the two sides now want different things; one wants to change things while the other wants to keep the status quo. That is far more dangerous than what we had in the past.
The other crucial difference is that for the danger of doomsday to exist back then, someone would have to make the decision to "push the button". Someone would have to decide to be actively responsible for armageddon. The danger we face now is opposite. If we don't take action this time then the predicted doomsday will happen by itself. Nobody has to press any button to make bad things happen. We are closer to doomsday because the button was already pressed years ago when we started down the path of rapid expansion of our use of fossil fuels.
The fact is that the doomsday clock actually worked during the cold war. It kept the issue in the minds of the people, so that the political will was there to solve the problem. The clock wasn't accurate nor inaccurate. It was a symbol.
In the same way, the changing of the clock isn't striving for accuracy in as much as it is raising the notion that we are facing a crisis in the public perception. And it is needed now more than ever.