juanrga, that's an interesting paper you mentioned. I found the preprint here:
http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9703/9703089v1.pdf
Just to make it clear at the start: In this paper, the guy is using the word 'axioms' to mean mathematical axioms (i.e. not to do with the philosophical meaning of the theory, but the actual physical core of it).
I think these 2 quotes summarise the paper pretty well:
Even in modern formulations MWI still seem seriously inadequate. Thus the aim of this paper is to argue that the literature neither contains nor suggests a plausible set of axioms for an MWI that describes known physics.
This means that the argument in the paper assumes that MWI must have different axioms to standard QM. So the guy who wrote this paper is talking about MWI as a separate theory to QM (not just a particular interpretation of QM).
The useful criticisms of MWI do not stem from an inability to accept the picture of multiple branching universes, nor do serious critics merely say that they do not see how to reduce macroscopic physics to an MWI. They assert either that particular physical facts are demonstrably not logically deducible from the axioms of MWI, or else they criticize the axioms proposed (usually on grounds of complexity or arbitrariness)
At the end of this quote, he seems to imply that it is possible to make MWI a different theory to QM and to make it agree with known physics, but then this makes the axioms complex/arbitrary. So this is a philosophical argument against MWI. (To paraphrase: 'yeah, it works, but I don't like the axioms.')
For most of the paper, he provides a few possible axiomatisations of MWI (as a separate theory to QM) and then shows that they each fail as a theory. So he's not providing a technical argument against MWI as an interpretation. He's providing technical argument against MWI as a different theory.