Apollo came dangerously close to losing a crew in several ways. There's Apollo 13 of course. There's also the POGO oscillation problem in the Saturn V which came close to destroying the launch vehicle. Then there's the lightning strike on Apollo 12 that came fairly close to catastrophe.
But aside from all that the biggest danger was a large solar flare while the astronauts were on the surface of the Moon. That could have quite easily exposed them to lethal radiation levels.
I may have made a mistake: risky and methodical are orthogonal. Space flight is inherently dangerous and the thousands of smart NASA workers were surely aware of the natural dangers, but their jobs were to minimize them. Thus, the apparent orderliness.
It's still incredible to me that Apollo 13 was the worst outcome and that the Apollo program, overall, ran "on schedule".
But aside from all that the biggest danger was a large solar flare while the astronauts were on the surface of the Moon. That could have quite easily exposed them to lethal radiation levels.