The person who wrote that paper doesn't understand the basics of the field that he's talking about.
For example (from the blog post): "Consa gives an analogy wherein Indian mathematician Srinivasa Ramanujan has claimed that the sum of all positive integers is not infinite, but is instead -1/12. It’s wrong, it’s absurd, but renormalization has now been accepted, and is even sold as a virtue."
One when performs zeta function regularization, one gets -1/12. This isn't some mystery; it's a perfectly reasonable thing to do. Analytic continuation has been understood since the 1800s.
Reference: https://en.wikipedia.org/wiki/Zeta_function_regularization
Edit: I read more of the linked paper. The claim that Karplus and Kroll committed "fraud" is basically libel, as can be seen by reading the complete account. The worst one can say is that people didn't publish full details of calculations due to page limitations or laziness, but this is hardly a special feature of QED. For instance, Onsager famously solved the 2-d Ising model exactly in 1944 but never provided details in print, just the final solution.