Concerning
It is a bit of an overstatement to call them "mistakes". Both
principles work great and are satisfied to the highest precision we
could achieve.
we can say the same for Flat Earth theory: it works great in everyday life, but it was a scientific mistake. A Flat Earth worldview would avoid the use of satellites among other engineering advances. A worldview where the above-mentioned mistakes are taken for granted may prevent new scientific revolutions, e.g., S. Wolfram was able to propose a way to travel faster-than-light by overcoming the mistake of considering spacetime in the same way as H. Minkowski did. There is a way to experimentally test that spacetime is not as H. Minkowski proposed, but as S. Wolfram proposed: measure whether the interior of a black hole causally influences its environement (if this happens, then faster-than-light travel was realized in nature). In other words, in the Wolfram Model, black holes are just an approximation, they are not absolutely black, since there may be microscopic space tunnels between the interior of the black hole and the exterior.
Concerning
As far as I know, writing Shroedinger's equation for the general wave
function (as opposed to amplitude and phase separately) requires only
linearity and unitarity of the evolution. Does Wolfram model violate
any of those?
at the end of the paper
J. Gorard, “Some Quantum Mechanical Properties of the Wolfram Model,” Complex Systems, 29(2), 2020 pp. 537–598.
https://doi.org/10.25088/ComplexSystems.29.2.537
the time-dependent Schrödinger equation (equation (152)) is derived as a variation of the diffusion equation in graphs. Notice the role of the branchial space, related to phase (page 589):
Our diffusion equation assumes the form of a Schrödinger equation
rather than a regular heat equation because of the presence of
imaginary branchlike distances in the discrete multiway metric.
This graph-theoretic approach is a proposal to overcome the restrictions (no-go theorems) of traditional physics, based on the mathematics of the continuum.