If you think doom is very probable and we only survived due to the anthropic principle, then you should expect doom any day now, and every passing day without incident should weaken your faith in the anthropic explanation.

What if you can see the doom building up, with every passing day? :-)

If you think all possible worlds exist, then you should expect our small bubble of ordered existence to erupt into chaos any day now, because way more copies of it are contained in chaotic worlds than in ordered ones.

I think this one is deeper. It is a valid criticism of quantum MWI, for example. If all worlds exist equally then naively all this structure around us should dissolve immediately, because most physical configurations are just randomness. Thus the quest to derive the Born probabilities...

I don't believe MWI as an explanation of QM anyway, so no big deal. But I am interested in "level IV" thinking - the idea that "all possible worlds exist", according to some precise notion of possibility. And yes, if you think any sequence of events is equally possible and hence (by the hypothesis) equally real, then what we actually see happening looks exceedingly improbable.

One pragmatist response to this is just to say "only orderly worlds are possible", without giving a further reason. If you actually had an "orderly multiverse" theory that gave correct predictions, you would have some justification for doing this, though eventually you'd still want to know why only the orderly worlds are real.

A more metaphysical response would try to provide a reason why all the real worlds are orderly. For example: Anything that exists in any world has a "nature" or an "essence", and causality is always about essences, so it's just not true that any string of events can occur in any world. Any event in any world really is a necessary product of the essences of the earlier events that cause it, and the appearance of randomness only happens under special circumstances (e.g. brains in vats) which are just uncommon in the multiverse. There are no worlds where events actually go haywire because it is logically impossible for causality to switch off, and every world has its own internal form of causality.

Then there's an anthropic variation on the metaphysical response, where you don't say that only orderly worlds are possible, but you give some reason why consciousness can only happen in orderly worlds (e.g. it requires causality).