The authors "show" that all supersymmetric gauge theories are inconsistent and anomalous. How do they achieve this difficult goal that would return physics 30 years into the past and debunk roughly 20,000 papers, all but demonstrating that all of their 3,000 authors or so are complete idiots?
Well, it's easy. First, they return physics 80 years to the past. They explain that Feynman's path integral is not "satisfactory". The only satisfactory treatment of physics must be based purely on the formalism that Heisenberg was using in 1926 for the harmonic oscillator, they postulate. Quantum field theory is not allowed, especially not the functional methods, FP ghosts, and renormalization.
So they write various commutators, being as careless about the UV subtleties of coincident operators as possible. Finally, they derive the "anomaly" (3.38) at the second order. You may think that the second order means two-loop level but that would be wrong. Recall that there are no loops and no Feynman diagrams here.
The form (3.38), containing two copies of the structure constants, could be related to a 1-loop diagram involving FP ghosts (or their superpartners, because the authors claim that (3.38) is a purely supersymmetric anomaly).
I think that it's fair to say that this completely flawed reasoning is an example of wider algebraic quantum field theory. Sometimes it is a good idea to attend standard courses of quantum field theory and learn how physics of gauge theories works in reality and why the anomalies are obviously absent in SUSY QCD and all similar theories. What this calculation may show is that it is likely that a consistent algebra of operators for gauge theories may be impossible without including things such as the FP ghosts. But such a result is not against supersymmetry; it is against naive algebraic quantum field theory understanding of physics of quantum field theories.
Moreover, their very idea that the supersymmetric gauge theories have additional anomalies is completely absurd. Supersymmetric gauge theories are not a new class of theories: they're a special example of otherwise ordinary gauge theories, with a special choice of spectrum and interactions that secures an additional symmetry. If all supersymmetric gauge theories had gauge anomalies, surely all gauge theories would have to have these anomalies, too.
An anonymous reader has predicted that Bert Schroer would endorse this crackpot paper and indeed, Schroer did so here.
