RE: Can we trust peer-reviewed papers?
I have watched the video and I agree with (in general) the sentiment of 100% of points the narrator makes. Your title is a misrepresentation of the point of the video however. It's point was not that there is something wrong with the peer review process, on the contrary, it's point was that the traditional editorial and peer review scrutiny of classical science journals is the best mechanism we have to ensure trustworthy data. Which is true. It is not the only mechanism, and it is not without it's faults and issues however.
The video also goes on at length about open access publishing, at this I draw some issues because there are some open access publications which undergo as much editorial scrutiny as the closed access subscription journals, some of which are run by the same editorial offices as companion journals (nature, science, cell, and a plethora of other high quality editorial offices all have open access journal branches, and the data is as trustworthy from these journals as the parent journal, however the topics just lack the "impact" aka sexyness of work put out in the subscription services).
In short, yes, you can trust peer reviewed journals, so long as they are run by a good editorial office, and get a lot of citations from the scientific community. However not all open access journal are run this way, some really are pay for play, while claiming to be "peer reviewed". It is for this reason that checking a journals impact factor can be useful. Is it a true criterion of what work is better? No. Is it a way to provide evidence for what might be bullshit (in the case of a publication in a very very low impact journal, aka one that researchers never cite)? Yeah it is.
Did you notice I used the exact same title as the video? When I share content from elsewhere, I think that's the best approach so those familiar with the content may already know what I'm sharing.
But yeah, as others have commented, he was a bit hard on the pay per play (as he should be, I think) but maybe could have spent some time on how important open access to information is, if we can figure out a good motivational system to keep the quality high.
Then his title is a clickbait misrepresentation of the point he is making in his own video. ;)
Definitely, and he should be.
As I said above, there are plenty of examples of open access publishers with very high editorial standards. The issue is not with open access, it is with fraudulent journals.