Peter Woit in Not Even Wrong:
Beyond Falsifiability blog post here.
Much of the problem with the paper and blog post is that Carroll is arguing against a straw man, while ignoring the serious arguments about the problems with multiverse research. The only explanation of the views he is arguing against is the following passage:
a number of highly respected scientists have objected strongly to the idea, in large part due to a conviction that what happens outside the universe we can possibly observe simply shouldn’t matter [4, 5, 6, 7]. The job of science, in this view, is to account for what we observe, not to speculate about what we don’t. There is a real worry that the multiverse represents imagination allowed to roam unfettered from empirical observation, unable to be tested by conventional means. In its strongest from, the objection argues that the very idea of an unobservable multiverse shouldn’t count as science at all, often appealing to Karl Popper’s dictum that a theory should be falsifiable to be considered scientific.
The problem here is that none of those references contain anything like the naive argument that if we can’t observe something, it “simply shouldn’t matter”, or one should not speculate about it, or it “shouldn’t count as science at all.”
More here.