Part of the problem with retractions is, I believe, that there's no middle ground. The article mentions several times that if a paper is retracted people will assume some kind of research fraud. A retraction is stigmatising and people are very reluctant to retract unless forced to as a result. It doesn't help that you lose a publication that took months, perhaps years, to put together.
Perhaps fraud should be the only reason to retract a paper. If the paper is invalid due to honest mistakes then it may be better to let the paper stand, but with a correction and addendum that makes clear what results are invalid, why they are wrong, and what the correct results are. Mistakes — especially mistakes that are serious enough to invalidate a paper, yet subtle enough not to get caught before publication — are an important source of knowledge in itself.
If people are reluctant to do corrections, then why not make a substantial, informative correction and reanalysis count as a publication on its own? That ought to give people a bit of incentive to do a good job with it.
The other big problem is that corrections and retractions aren't widely announced, and the information doesn't really trickle down to people using the paper. The article only touches on it, but once you've downloaded and read a paper you're very unlikely to revisit the original site again. Why would you, after all? And with the flood of new papers showing up every day you can easily miss a correction or retraction notice in the deluge. Retracted or corrected papers end up being used for many years after they should have been dumped. I don't have a good idea for how to fix that.
But I don't think the resulting problems are all that dire. Your typical paper has two kinds of references, really: the main sources, and a bunch of supplementary ones. Your main sources are really significant. They're the ones you're really building your work on and without them your paper falls apart. The supplementary sources are more about dotting i's and crossing t's; you're showing that you've read the literature and use them as support for minor points in your work. If one of them happens to be wrong1 it won't actually have much of an impact on your paper or your work.
And of course you're lot better informed about events surrounding your core references. You seek out and read other papers that reference the same work; you follow the same journals they appeared in; and you keep an eye open for more publications from the same group. If one of your core references are retracted (or simply shown to be incorrect or incomplete) you're quite likely to find out.
This is a general principle, I think: if an important paper is retracted it is a serious matter, but many people will quickly find out and knowledge of it will rapidly spread. If a paper is retracted and nobody notices, on the other hand, then it wasn't much of a paper to begin with and the damage is minimal.
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#1 It's worth noting that it's common to find several papers about the same exact thing that all disagree with one another. We deal with, and make use of, potentially incorrect papers on a daily basis and have always done so. We know our sources are not some infallible truth, and the sky doesn't fall when a paper or two turns out to be incorrect.
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