Most Americans would nominate something to do with the Iraq war, or perhaps the economy, as George W. Bush's greatest error. That will hold up for 20 years, I think, but later observers will call them successes. The Iraq and Afghani wars, or something very like them, needed to be done and he did them. Arguments about how well he did them or whether someone else could have done better will become irrelevant. Counterfactuals are interesting in their approximate time period, but soon become science fiction (not that that's a bad thing). Al Gore would have done something different - or not. Kerry would have gotten us out sooner - or not. My own take is that we now know the UN was never going to provide support, and the UK supplied good soldiers and bad strategy - we would have done better to simply go in ourselves in 2002, and who knows what we might have found before Sarindar (google), eh? Certainly, everyone wishes we'd ditched Bremer and found Petraeus sooner.
Vlad Putin was George Bush's big mistake. Russia was bleeding and half-dead on the floor after the breakup of the USSR. Yeltsin, for all his faults, looked like he was trying to bring Russia into the community of half-sensible nations, and we encouraged this. But Bush met with Putin in 2001. "I looked the man in the eye. I found him to be very straightforward and trustworthy and we had a very good dialogue. I was able to get a sense of his soul..." Vlad Putin ate his lunch over the next 7 years. After 9-11, we appealed continually to Russia to help defeat, or at least not actively assist, governments sympathetic to jihad. We needed Putin to do this and kept overlooking any infraction in the hopes of winning them to decency. He played us well.
It was a noble mistake. It was an offer to reach out and treat Putin and the Russians decently in spite of past conflicts, in the hopes that they would respond to our good will and become more decent themselves.
Isn't that the approach the Bush critics have advocated we apply to every nation? Isn't it progressives who often believe (minus the sensing of his soul) that this is what works in the family of nations? The religious left, at any rate, has frequently advocated such approaches.
I will not overgeneralise about liberals on this one. There were plenty who counseled more caution, even suspicion of Russia on this score, and were critical of Bush for being too trusting. Many isolationists and Realpolitik types were approving of this action of Bush as well: just do business with people and don't blather on and try to interfere in their affairs. But those people who say if we don't want terrorism, we shouldn't terrorise; who call Bush a provocateur and aggressor and assure us if we stopped thinking of other nations in terms of good and evil that we'd see them come 'round to jolliness - don't those people usually vote for Democrats?
Putin has been remarkably successful at making Russia a power again, in the old style. Whether he can continue to be disciplined and not overreach, whether Putin turns out to be enough for a failing and unstable country, and whether the Russians have any more like him after he's gone remains to be seen. We can hope not, and will perhaps have a chance again to invite the Russians into the community of half-sane nations. But for now we are back in danger again.