My impression is that MW vs. other theories are not a disagreement about the math, but about how the math should be interpreted.
Doesn't that actually put the question out into philosophy? (specifically ontology in this case, I think)...because, without really knowing much about the physics, it seems to me that the whole disagreement stems from not defining the word "reality" rigorously enough.
Essentially, I suspect that we should be able to make a simplified model that doesn't involve extremely complex math, which showcases the disagreement inherent in MW / copenhagen / etc so that non-physicists can think about the problem.
...And I might be completely wrong about that, because I don't know physics...I'm drawing my conclusions mostly from the pattern of disagreement that I see in discussions involving this issue. It's the sort of pattern that arises from a philosophical dispute rather than an empirical one.
My impression is that MW vs. other theories are not a disagreement about the math, but about how the math should be interpreted.
Just sticking to the quantum interpretations discussed in the sequences, Everettian/MW quantum mechanics has 1 fewer postulate then Copenhagen quantum. The question as to whether they are empirically identical is still open- no one has derived the Born probabilities in many worlds. Until someone does, no one really knows what many worlds predicts. Most pop-science sweeps this under the rug- including the sequences.
The inability to derive the Born probabilities is THE key area where many worlds fails, and its a technical problem with the physics/math.
There are a great many ideas which don't have enough carefully-measured evidence to be sufficiently confirmed as scientific fact and accepted as such by the scientific community (a recent joke was "While the Higgs Boson has not been discovered yet, its mass is 125 GeV"), but don't have enough carefully-measured evidence to be ruled out yet, either. Do any of the tools of the LW community help narrow down which ones are more worthy of consideration than others?
Eg:
* Cryonics as an arguably reasonable bet for its cost: proto-science
* Cryonics as a surefire way to achieve immortality: nigh-certainly pseudoscience (unless it's the method by which your Everett Immortality keeps you alive)
* Using math to demonstrate that taking classical physics and adding determinism results in MWI-style quantum physics: proto-science.
* Using math to demonstrate that quantum physics proves Christianity is true, from a certain point of view: pseudo-science
* Tubulin might self-organize into microtubules capable of computation on a sub-neuron scale: Possibly proto-science
* Tubulin architecture is 'quantum' in nature and that is what gives rise to consciousness: Probably pseudo-science
* 'Quantum consciousness' means anything is possible: Downright silly
* The E8 Lie group can provide a system for organizing the properties of subatomic particles: Proto-science, perhaps
* Heim theory is useful for predicting particle masses: Pseudo-science, probabilistically
* Using the Bullet Cluster to claim that dark matter is a better theory than Modified Newtonian Dynamics: proto-science
* Claiming that dark matter is made of 'anapoles': Proto-science, perchance
* Suggesting that dark matter is actually gravitational leakage from MWI 'parallel universes': You tell me. (But if it's true, then since I can't seem to find any previous serious discussion of this idea, I get to name part of it after myself, right? :) )
These may not be the best examples, but they're the closest ones I can think of to the boundary. If you know of any better ones, feel free to comment with them.