Question: Is it possible to get a refund from a publisher if I bought an article that contains a major flaw (i.e.,one that invalidates the main results or the main conclusions)? Assume the article was bought through one of the main academic publication's paywall.

Answer: 
Of course you can request one - just send an email. You'll brighten up the publisher's office for the afternoon, and they'll be chuckling all the way home.

So just as long as you don't seriously expect to get your money back, you'll be fine. When you paid your fee, you were paying for access to read the paper. As long as that access was provided, then the publisher has met their side of the bargain. Peer review is not a guarantee of correctness. It's a first-level junk filter, nothing more.

And on top of you getting what you've paid for, you've got the additional bonus that you've now got a new paper that you can write, that's practically already written itself; the paper where you take apart your bought paper's argument. Magnanimously, the publisher won't require you to pay extra for this bonus - you got it thrown in for free.
You can ask for anything you want, but you will not get a refund. The terms and condition of the site where you purchased it most likely clearly stated that it wasn't an option.

One example from Taylor & Francis:

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> The content in this site is provided "as is" and without warranties of any kind either express or implied.
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> Taylor & Francis Group Ltd do not warrant or make any representations regarding the use or the results of the use of the content in this site in terms of their correctness, accuracy, reliability, or otherwise.
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And another piece of sound advice:

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> If you do not agree to these terms, please do not use this site.
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More generally, the money you pay for the article is strictly for its publishing, the actual research that resulted in a "major flaw" was paid via other channels, on which it's very unlikely that you'll have any direct influence. The people making the original claim about the content of an article, and taking responsibility for it, are *the authors* not the publisher to which you paid the fee.

If you witness that a given journal has consistently low acceptance standards, make sure to notify your institution's library, they might consider resigning subscription if they gather enough similar complaints.

Sadly, for the occasional 20 bucks you consider wasted for that article (I'm sure this is purely fictional, there are many ways of getting subscription journal's content without paying for it) there are 10 unscrupulous scholars, somewhere who use 3000$ of your tax money to publish complete rubbish in an open access journal. And here the perspective of a refund is nonexistent.