I agree that there are real structural issues, especially in certain fields, and especially involving the incentives for funding and publishing. However, I think that the overall impression gives some mis-characterization, at least from my perspective as a molecular biologist / geneticist.
First, I think that the most prominent studies are the most likely to have issues; generally they're doing something new, often with new methodology. It's here where extrapolations tend to be made that are the most dangerous. It's also not surprising that social sciences have such issues; they don't have rigorous tools (i.e. genetics) that can effectively ground their work. It makes compounding issues much harder to catch.
Related is the re-testing issue; in many fields, subsequent work will catch errors in previous work. If you work with a mutant and then someone else works with it, they'll see if it behaves differently than expected from the previous work. Germplasm travels, and it's the ultimate arbiter of truth. This usually does lead to further scrutiny and fixing the issue. The real problem that I've observed isn't that the errors aren't caught, but that a formal retraction isn't always done. Sometimes it just gets contradicted in a subsequent paper (and often with some relish) without ever resulting in a retraction. The editors of that journal clearly have a responsibility here that they are failing to uphold.
However, despite these faults, it's quite clear to those of us with 'boots on the ground' that you can't hide from the data; as long as you're using solid genetics and doing 'real' experiments (e.g. western blots, in situ/immuno-localization, simple gels/pcr, etc.) you can only hide for so long. The exception is if no one keeps working on it, in which case it's probably not that interesting to begin with. This also leads to a deep suspicion of bioinformatics among geneticists because we see how often things go wrong, and what is needed to make it right. Fortunately, genetics can still be used to great effect.
Ultimately, I'm not suspicious of the large body of work in my field. Most of it is based on extremely solid forward genetics that withstands lots of testing. Even now, great value is placed on these 'old school' methods because of how robust they are known to be.