Sorry to say, but this critique of Schroeder is as much bullshit as some of the stuff that Schroeder expels. There is nothing wrong with the given equation, and suitably re-written gives the Compton wavelength for a particle, assuming m is the rest-mass. I haven't read the relevant Schroeder work, so I cannot say in what context he was using this, but Perakh's complaint appears completely unjustified. Perakh also appears very juvenile in various other areas - such as his complaints about the use of centrifugal force and the rest-frame of a photon.
This is the problem when real physicists are too busy and too jaded to be bothered countering mumbo-jumbo - the job gets picked up by those insufficeintly qualified/experienced to do the job.
Now Oser does a reasonable job, as one would hope given his background, but even here his critique is a little off perfect in a few areas...
In the case of a photon then planck's constant disappears?
No, because we are talking about massive particles, not massless particles. This is already established in getting to where m is rest-mass, as I previously stated. If we're dealing with a massless particle, we don't have this relationship, as it is not possible to bring that particle to rest.
In your rearrangement with h on the lhs, you have to realise that as you vary m, you must also vary f.
The wave length of the scattered photon would be constant given the constant rest mass of the particle.
No. The Compton Wavelength is not the wavelength of the scattered photon in Compton Scattering, merely related to it (the three factors are incident wavelength, angle of incidence, and the CW.) Go study the process and you will see.
f would also be constant for any specific mass.
Yes - that is the whole point of the Compton Wavelength.