1. Conservation of energy. 2. Relativistic observers seeing multiple decoherence events in different orders. 3. Experiments that affect whether a particule pair did decohere inthe past. (i.e. quantum state recombination.)
Basically, MW assumes that the probability wave exists and that all outcomes exist, which is a very big assumption, which that FAQ gloss over rapidly. (And then explictly call other interpretations' assumptions as a negative...)
This is not a problem for MWI.
> 2. Relativistic observers seeing multiple decoherence events in different orders
There is no decoherence in MWI.
Yes there is. Decoherence provides the theoretical framework to explain why the superposition of parallel observers can never meaningfully interact with themselves again, even though a superposition of simple particles can.
See https://en.wikipedia.org/wiki/Quantum_decoherence#In_interpr... for more.
That said, the order in which an observer notices decoherence events has no particular physical importance.