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Wheeler himself made some rather extraordinary claims which take the nature of observation far too seriously. If he had limited himself to saying "our perception of the past is determined by our measurements," that would have been rigorously acceptable. In claiming the past itself is shaped by measurement he claimed a bridge too far.

The experiments carried out so far are not much different from polarization experiments which verify Bell's Theorem or, if you prefer, the EPR Paradox, which is really a strange result, but no paradox at all.

Couple things to keep in mind here.

First, a lot of the literature on this subject is very confused, much like Schroedinger's Cat and EPR. People are simply not careful enough to draw the conclusions they've claimed. Second, Wheeler never went as far as to say there would be Lorentz frames in which a quantum measurement would violate causality. He came very close but never said so. Third, that eigenstate into which a state vector collapses upon measurement is a stationary state of an Hermitian operator. There actually is no operator corresponding to "looks like a wave" or "looks like a particle" and that's a GOOD THING, because the state vector (or wave function, if you prefer) of a quantum system is NOT (despite elementary analogies made in junior high to the contrary) "sometimes a wave" and "sometimes particle" it is always one thing: a state vector, which completely describes everything we can know about (say) a photon. That's all you get, and that's all there is, and it isn't sometimes one thing and sometimes another.

I think a lot of people are drawn into the "isn't causality violated by this" trap by a fundamental misunderstanding which arises from examining pointlike behavior, which is an illusion. Quantum systems do not "behave" as trajectories evolving from point-to-point in the absence of constraint, which behavior can sometimes lead to paradoxes when we change our methods for measuring them or when we consider entangled systems. This is falsely claimed as a unique feature of quantum mechanics. Actually, it isn't. Classical mechanics also has this feature. In his (in my opinion, highly overrated) graduate text on advanced Classical Mechanics Goldstein actually comments on this in the context of refraction.

Even in classical physics, light takes the path which involves the shortest physical distance between two points, which is why (for example) a ray of light bends toward the normal when a relatively higher refractive index is placed between the source and destination. How does the light ray "know" bending toward the normal will shorten its effective path? How does it "know" that it's time to stop doing this when the medium changes again?

In both classical physics and quantum mechanics, the answer is the principle of least, or "stationary" Action. And as Goldstein points out in his exposition of stationary Action in classical physics, "reflection on this often leads to pointless teleological arguments."

Just so.

What is happening is better understood via the Feynman Path Integral than via any other conceptual or theoretical tool. The Feynman Path Integral formulation works just great in classical physics, too, and it leads to "correct thinking" about these things. A physical particle's state vector literally travels every conceivable path through space time, and the trajectory which minimizes its Action is the one that ultimately is observed. New measuring instruments, silvered mirrors, half-silvered mirrors, microwaved atoms, or whatever else you want to throw into its possible paths will factor into that outcome, throughout all of spacetime.

So, why do these point-to-point interpretations seem to fail so miserably when we do thought experiments, when they are, in fact 100% equivalent to the Feynman Path Integral?

The answer is that constraints are cooked into the motion. As is the case with any good magical act, preparation is everything, and the rabbit goes into the hat long before people are watching. The failure of "local realism" is a failure of inattention on the part of the audience. A light ray bends toward the normal, following the path of least Action because a light ray is constrained by an equation (the Klein-Gordon Equation) which determines the behavior of light throughout ALL OF SPACETIME. And this is the part that people forget when they allow themselves to be tricked by these apparently "non causal" or "non locally realistic" theories.

These theories are NOT LOCAL TO BEGIN WITH!

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This "surprising" outcome is well understood by mathematicians, but occasionally forgotten by physicists. The behavior of a twice differentiable function throughout any volume of space is entirely determined by what happens on its boundaries. Once you have set what happens on a boundary, nothing the function does anywhere else has any real freedom.
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Same thing with electrons. In non-relativistic quantum mechanics, you have the Shroedinger Equation, which, again, permeates all of space for all time (non-relativistic, so space and time are not codependent.) In relativistic quantum mechanics, the Dirac Equation does the same thing.

Because in the Feynman perspective, you are integrating the Action throughout all of spacetime, you can't forget about the constraining equations, which always apply, and which rule out strict locality.