It's not clear that 'MWI' in the LW sense has very much content -- in particular, it's not clear that Eliezer is committed when he endorses MWI to Carroll's description above. His recognition of the mysteriousness of 'reality fluid' and his willingness to entertain ideas like mangled worlds suggests he's perfectly happy to modify QM to generate the Born probabilities, provided the modifications reflect the character of physical law better than Bohmian Mechanics and objective collapse do.
If MWI is just 'Bohmian mechanics is wrong' plus 'objective collapse is wrong' plus 'the right answer will structurally resemble our current physics', then the best articles criticizing MWI might be ones that defend Bohmian mechanics or an objective collapse theory as non-ridiculous, and argue that until we have a finished empirically adequate MWI we can't be confident it will actually turn out simpler or more-in-the-character-of-physics than BM.
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I'd be even more glad to read an article that specifically is against MWI/Everrett (or whatever you call it).
David Wallace, The Emergent Multiverse, Interludes I and II, presents both sides but in the end is pro-MWI.
A coherent, intelligent, reasonable article by an advocate of the other side would make things clearer.