One thing I don't understand about Psychophysical Parallelism, is that it states that the mind and body are perfectly coordinated, yet there is no causal relationship between them. If this is true, then how do they explain the perfect correlation, would it be just a coincidence?
This would (from the point of view of people who defend the parallelism approach, at least) be sort of like asking how "mass times velocity" and "momentum" stay perfectly coordinated if there is no causal relationship between them. Mass times velocity doesn't cause momentum, it defines momentum (at least, it did in classical mechanics). (With respect to causality the goal is to show that the causal consequences of a system with a certain momentum are consistent with the causal consequences of a system of point masses with the corresponding velocities; whether psychophysical parallelism must have some concept corresponding to this goal is not entirely clear, but Leibniz's famous version of it did.)
This is not to minimize other possible problems with parallelism, but if you think that body "causes" consciousness the way your computer "causes" pixels on the screen to light up, you're not actually considering the parallelism hypothesis yet.