Academic literature has many problems but it is way above the blogosphere in that regard. And media coverage is going to suck no matter where stuff is published...
From the perspective of peer review, yes. But per google scholar that paper has been 66 cited times, including in many articles that are in at least somewhat reputable journals (published via Elsevier, ieee, Springer, etc) and apparently two books [0]. So I think it's pretty clear that being a "scientific paper from Princeton" was significant reputation wise regardless of whether or not it was peer reviewed.
[0] https://scholar.google.com/scholar?q=Epidemiological%20model...
I was also skeptical about the citations so I checked that two with freely available pdfs were actually this paper, they were
[1] https://pdfs.semanticscholar.org/4ebb/b654c59aff454ad97301e6...
Some papers are cited not because they are well written, but simply because they covered a topic which might not have been covered by other researchers. Literature review is a fundamental part of a paper.
I also know a guy who published preliminary results and musings on his blog, and was then refused publication because it was "unoriginal".
Journal editors seem to not be familiar with the subject matter either, given what does and doesn't get published - why only ever positive results?
Unless scientific publication changes completely science as we know it will die. It is already becoming vanity, egoism, orthodoxy. Why publish? So you can get better pay later in the private sector.
1. George Box has a very famous quote: "All models are wrong; some models are useful."
2. Even the model applies correctly for Myspace, it does not mean it is correct for Facebook. I would use a very common terminology - "survival bias/selective bias" for it. The only way to ensure the model is letting it through numerous amount of cases. There is not only one social network is active, can the author predict for them and for the old one? Here is the possible list: https://en.wikipedia.org/wiki/Social_networking_service
3. When they cited a paper, they are not supposed to agree with them. Some of paper even criticize each other. They may accept the concept of Facebook being cool down but not in couple of years (with different parameters). If you want to make sure they are all agree or not, please make a survey on this. Like I said, you (and probably me) are probably into survival bias.
4. There is a least one mistake here: "discussed in Section ?? [3],". So, was it well proof read?
Peer review, looking at it from the outside as a layman, appears to just be an enormous rubber stamp. I cannot believe that academics have time to rigorously go over the mountains of pages of dreck that make up most research papers, and even read the whole thing thoroughly, much less double-check the numbers. Not when they have a stack of papers to review a foot high, and another two feet of grants to write, their own research to do, not to mention what little teaching they haven't farmed off to grad students.
Had it been a blog post, I don't think anyone would have taken more than a cursory look at the analysis. Yes, anyone can fit data points and reach a conclusion with blogs, but isn't academic research fraught with similar problems already?
[1]: https://www.theguardian.com/technology/2014/jan/22/facebook-...