How, though? Assume a particle has some Flatten() method that is called only when it interacts with another particle. Until this is called, certain data points (let's say, anything not related to it's movement through space) could be either undefined or out of date.

When this function is called, it causes some algorithm to set up these data points. You can extend this to treat entanglement as copy-on-write style branching, where entangled particles A and B have some subset of their properties stored in the same physical memory, but calling this methods causes writing to those properties, and, thus, when the function is called for particle A, a copy of the properties is made for both A and B, and the evaluation is done for both.

You're assuming that movement properties are special, and that non-movement properties don't affect the environment until they are collapsed. This is not the case -- quantum mechanics treats all quantum properties in the same way. An indeterminate spin can be detected in the same way an indeterminate position can be detected (i.e. indirectly, via diffraction and interference effects). It is true that if particle A and B are entangled so that spin A + spin B = 0, then that may help you optimize your "universe computer", but it doesn't gain you much since any gains will be offset by needing to store the fact that A and B are entangled. Not just that, but you have to take into account the fact that any number of particles can be entangled, with any arbitrary linear combination of properties.

IMO the biggest reason to think the universe isn't a computer is just how darn non-computable quantum mechanics is. The complexity grows at an absurd rate. Even for just the position of two particles you have a 6-dimensional wavefunction with (as far as we know) an infinity of possible values for every (infinitesimal) point in that 6-dimensional state space.

>the biggest reason to think the universe isn't a computer is just how darn non-computable quantum mechanics is

If an intelligence is simulating a universe, they aren't exactly going to be doing it von-neumann style.

That's a good point, but the fact that all Turing machines are equivalent (and the fact that the equivalence is purely mathematical, and does not rely on any laws physics) implies that computers in ANY universe would be similar to ours. At least in terms of what it can compute. Even if the laws of the parent universe made their computers dramatically faster than ours, you would still expect that they would choose our universe's laws of physics so that they were relatively easy to compute, so as to save CPU time. That doesn't seem to be the case -- it takes us a supercomputer to accurately simulate a volume a fraction of the size of a proton. Of course this doesn't prove anything -- it's possible that computers in the parent universe are so ridiculously powerful that even simulating a trillion galaxies is just a drop in the bucket -- but IMO it is suggestive.