The entire Reinhart-Rogoff fiasco reminded me of my post from last year on how empirical evidence is overrated at times by a chart-happy blogosphere. Reading Nate Silver's book gave me a better way of putting this. In his chapter on climate change, he makes the point that one reason climate change skepticism is so tenacious is that the statistical data about climate patterns really is a bit on the noisy and ambiguous side. The reason you can know that the skeptics are wrong isn't so much because the data is so overwhelmingly persuasive, it's that the data is overwhelmingly persuasive in light of the underlying science of how greenhouse gas emissions would cause climate change. Absent the causal theory about the greenhouse effect, simply looking at a chart of world temperatures and the correlation with CO2 emissions wouldn't prove very much. The empirical data is important because it's in line with the predictions of a persuasive theoretical account.
The R&R situation is basically the opposite. In the absence of a plausible account of why a high debt:GDP ratio would cause slow real growth even in the absence of high interest rates, you would want to see overwhelming empirical evidence for the existence of such an effect before you believed it. And they just didn't have the goods.
In general you're going to find that most empirical world in a field like economics is subject to some considerable uncertainty. It's very difficult to run proper experiments, and when you can run proper experiments the relevance to the real world isn't always clear. So when you look at a purported empirical finding you need to ask not only how strong is the evidence, but what's a reasonable prior assessment before looking at the new empirical data. A correlation is never sufficient to establish a causal relationship, but it might be good evidence for the existence of one or else it might not. That depends, in part, on how strong your theory is. The only theoretical account backing the R&R causal inference was a kind of hazy moralism, which should never be good enough.