If a world splits, the energy of each split-off world would have to be less than the original world.

No, you are misunderstanding the argument. I am a MWI opponent but I know you are getting this wrong. If we switch to orthodox QM for a moment, and ask what the energy of a generic superposition is, the closest thing to an answer is to talk about the expectation value of the energy observable for that wavefunction. This is a weighted average of the energy eigenvalues appearing in the superposition. For example, for the superposition 1/sqrt(2) |E=E1> + 1/sqrt(2) |E=E2>, the expectation value is E1/2 + E2/2. What Q22 in the Everett FAQ is saying is that the expectation value won't apriori increase, even if new worlds are being created within the wavefunction, because the expectation value is the weighted average of the energies of the individual worlds; and in fact the expectation value will not change at all (something you can prove in a variety of ways).

To use an extreme example, that's supposed to be why you can't see anyone in a world where the Nazis won WWII: That part of the wavefunction is so decoherent from yours that any interference is just random noise and there is therefore no meaningful interference.

Well, this is another issue where, if I was talking to a skilled MWI advocate, I might be able to ask some probing questions, because there is a potential inconsistency in the application of these concepts. Usually when we talk about interference between branches of the wavefunction, it means that there are two regions in (say) configuration space, each of which has some amplitude, and there is some flow of probability amplitude from one region into the other. But this flow does not exist at the level of configurations, it only occurs at the level of configuration amplitudes. So if "my world", "this world", where the Nazis lost, is one configuration, and the world where the Nazis won is another configuration, there is no way for our configuration to suddenly resemble the other configuration on account of such a flow - that is a confusion of levels.

For me to observe interference phenomena, I have to be outside the superposition. But I wasn't even born when WWII was decided, so I am intrinsically stuck in one branch. Maybe this is a quibble; we could talk about something that happened after my birth, like the 2000 US election. I live in a world where Bush won; but in principle could I see interference from a world where Gore won? I still don't think it makes sense; the fact that I remember Bush winning means that I'm in that branch; I would have to lose the memory for the probability flow here to come into contact with the probability flow in a branch where Gore won. More importantly, the whole world configuration would have to morph until it came to resemble a world where Gore won, for some portion of the probability flow "here" to combine with the probability flow there.

I'll try to explain what I'm talking about. The wavefunction consists of a complex-valued function defined throughout configuration space. Configuration space consists of static total configurations of the universe. Change exists only at the level of the complex numbers; where they are large, you have a "peak" in the wavefunction, and these peaks move around in configuration space, split and join, and so on. So really, it ought to be a mistake to think of configurations per se as the worlds; instead, you should perhaps be thinking about the "peaks", the local wavepackets in configuration space, as worlds. Except, a peak can have a spread in configuration space. A single peak can be more like a "ridge" stretching between configurations which are classically inconsistent. This already poses problems of interpretation, as does the lack of clear boundaries to a peak... Are we going to say that a world consists of any portion of the wavefunction centered on a peak - a local maximum - and bounded by regions where the gradient is flat??

But here I can only throw up my hands and express my chronic exasperation with the fuzzy thinking behind many worlds. It is impossible to intelligently critique an idea when the exponent of the idea hasn't finished specifying it and doesn't even realize that they need to do more work. And then you have laypeople who take up the unfinished idea and advocate it, who are even more oblivious to the problems, and certainly incapable of answering them.

Paul, if I could convey to you one perspective on MWI, it would be as follows: Most people who talk about MWI do not have an exact definition of what a world is. Instead, it's really an ideology, or a way of speaking: QM has superpositions in it, and the slogan is that everything in the superposition is real. But if this is to be an actual theory of the world, and not just an idea for a theory, you have to be more concrete. You have to say exactly what parts of a wavefunction are the worlds. And when you do this, you face new problems, e.g. to do with relativity and probability. The exact nature of the problems depends on how the MWI idea is concretized. But if you give me any concrete, detailed version of MWI, I can tell you what's wrong with it.