What is special about protein in egg white such that it denatures upon heating and then aggregates again, making it opaque? Is it possible to take protein powder solution (like from Power Shakes, etc), heat it up and observe the same affect? If not, is is because the mol weights albumin is so much higher than that in commonly used powders? Or phrased another way, "Can this effect be simulated with off the shelf protein supplements, or is this effect ONLY with egg protein?"

A lot of proteins denature when subjected to heat. It's usually because the energy input breaks various weak electrostatic bonds keeping it together (H bonding, etc) as well as other types of chemical bonds, causing it to lose its form. The reason that egg proteins change in their morphology is, I think, because when it cools it refolds in a different way to what it was prior to heating. Reason for that would simply because the conformation probably falls in a localized energy minima - not necessarily as energetically favored as it was before, but low enough for it to be stable.

Here's a nice animation on protein denaturation.