To answer the OP question:

The paper contains 3 examples of claimed problems with standard theory, which are solved by an idea giving particles travelling at speed c non-zero *rest mass*.

The OP asks for *errors *in this idea.

I see no errors, except that it is more complex than the normal theory (not an error, but undesirable) and, it makes no predictions distinct from normal theory that have been observed.

I do see errors, quite grievous ones, in the rationale for the paper which starts by highlighting 3 problems in standard theory.

The argument in the paper sort of makes sense if you adopt a particle-only view of photons. But, photons are (just) e-m waves. The energy of given e-m waves is very precisely and properly described, and related to the corresponding fields. One photon of a given frequency is well defined, in a cavity, and corresponds to a given energy based on its frequency E = hc/lambda where lambda is the photon wavelength. Lambda can be arbitrarily large, leading to energy arbitrarily low. thus for the photon energy to come from rest mass we would need an entirely different idea of rest mass, something that can be arbitrarily variable in a way that is different from all the rest of quantised physics.

Nothing wrong with that, except complexity (simpler for everything to work the same way), and lack of motivation: it makes no distinct predictions that have been observed.

The paper notes that Lorentz relativistic mass formula cannot be used to determine the mass of a particle travelling at c, since it shows a singularity. But that argument is silly. It is often true that one mathematical derivation leads to an undefined quantity when another one gives a correct and consistent asymptotically defined value. Using the argument here you would say that derivatives were undefined and a "problem" for mathematics!

There are many interesting alternate theories of fundamental physics published and commented on by mainstream science. Everyone sort-of hopes one of them will gain traction, because unlike what many here think (in a pseudoskeptical and contemptuous ignoring of the reality) physicists are profoundly and actively interested in new ideas. The ones highlighted here, without any traction in mainstream physics, seem attractive if you are disturbed by one or more of the profoundly counter-intuitive experimental facts of quantum physics. They produce semi-classical equivalent explanations with no merit except that they are "real physics". For example here the disturbing idea is that rest mass (as viewed as an interaction with a Higgs field that creates inertia) can be zero (no interaction) in which case particles travel at the speed of light.

The idea that a semi-classical explanation of quantum physics is "more real" than a quantum explanation is, in my view and that of most who have ever properly worked with QM and GR, profoundly reactionary and anthropomorphic. why should the fundamental physics of the world be familiar from the human-scale physics that we learn from playing cricket (er, for some, baseball) when young?

I see it as the opposite of what this site otherwise tries to do - being open to new unexpected ideas.