No military in the history of the world has done as much to prevent collateral damage (i.e. the killing of innocent bystanders) as the U.S. military. That is just a fact.
Historically, that's obviously untrue. In modern times, it is, at best, disputed. Many militaries have done far worse, of course. But starting in the 90s and continuing through the second Iraq war, the U.S. (not to mention its allies) has by many accounts expended less effort at protecting civilians than they had in former wars, not out of malice, but likely in an effort to instead minimize American soldier deaths at any cost and maintain public support for the war in the U.S. And of course, the safest soldier is one that's not on the ground where people are dying.
The shocker was how people were dying. For the first time, in any of his [war mortality] surveys, the leading cause of death wasn't disease. It was bombs and bullets. [...] And the biggest number [...] were killed by the American-led coalition.
"I should mention that only three of them involved guys with guns. All the rest were helicopter gunships, and bombs from planes. [...] There's no evidence here of soldiers running amok. There's evidence here of a style of engagement that probably has relied very heavily on air power that has resulted in a lot, a lot of civilian deaths. [...] A Pentagon spokesperson said that they've dropped about 50,000 bombs in Iraq. 50,000 bombs. Very, very small fraction of them would need to miss their target or be based on bad information to explain 100,000 civilian deaths."
– Les Roberts talking about the first Lancet Iraq War mortality study (covering the first two years of the war, and before sectarian violence began dominating mortality) on This American Life.
As the same story later goes in to, the Pentagon soft limit for acceptable number of civilian deaths was 30 per airstrike. (By that standard, I guess they were really careful, given that we didn't have 1.5 million civilian deaths from those 50,000 bombs...)