What errors in reasoning do we see here? "Free-will FALSIFIES Materialism & ATHEISM"

You can be an atheist "because boo" if you want. You do not need to believe in materialism, or vice versa. You could believe in God, and be a materialist. Maybe you think God can consists of matter, and he's the most powerful being in the universe, and somehow exists eternally. While that is not what any mono-theistic religions teach (that I know of), one could still define God as "the greatest existing being". They could then argue that of all beings that exist, there must be a greatest, and the greatest being that exists is God. A kind of Ontological Argument from existence. 

For hundreds of years, rational atheists predicted a materialist explanation of the universe would be correct. "Scientific-atheists" of the time predicted and believed that all ontological reality consisted of matter. Pierre Simon Marquis de Laplace was a great physicist and philosopher, one of the great polymaths who really developed the atheistic position. He recognized that physicists could calculate, explain, understand and predict matter in motion. All matter in the universe  is in motion, and since the universe was composed of matter, when science became sophisticated enough, we could track matter, it's trajectory, it's interactions, the chemical interactions that took place etc etc, and determine their outcomes. Thus the name "determinism". Since even the human mind is made up of matter, he argued, that would be determined too, just as certainly as the trajectory of objects in motion and chemical reactions. This was when most rational atheists called themselves "materialists", which they did until fairly recently.

Turns out he was wrong about just about everything. When Heisenberg Uncertainty was demonstrated to be true, everything Laplace believed (and many others) was false. Heisenberg Uncertainty states that at the smallest scale, the position and the momentum of particles cannot both be known at the same time. And of course there's still physicist who try to get around this, and there's probably over a dozen interpretations of QM, such as the Many Worlds or Everett interpretation, which posits that the apparent random position of a particle does not actually collapse upon observation, but splits into like an infinite number of parallel universes, in which every possible physical outcome is equally real. I guess in their minds, there's some actual universe that exists where I'm an atheist king, with 1000 concubines, and Richard Dawkins is the Pope, and horses really did evolve to develop a sing horn and wings. Anyhow... that's their way around it. Another way around it is that there's like immaterial abstract objects that exist, that are "natural" that control all of this (think of when you hear some physicist on the discovery channel claim that "maybe the laws of physics themselves are responsible" for this or that). They maintain someday science will uncover all of this, and prove once and for all that they were right all along. 

Today, most atheists who try to maintain some rational basis for their atheim have drastically moved the goal posts, and now refer to themselves as "Naturalists" and will be offended if you called them a "Materialist".  That is, the universe and everything in it has a "natural" explanation (whatever the eff that is supposed to mean). "Naturalism" is an utterly unfalsfiable proposition, and is the same as a religion, but that is their final defense. 

Good call on the alleged certainty.

A reminder to those of you who downvote answers: please comment as to why you think it is a poor answer.

 Does quantum randomness exist? If it does, this is compatible with materialism and would mean the determinism is not true, would it not? 

I would say that this is not the case. Determinism is the notion that events are caused by a prior event dictated by the laws of nature. The laws of quantum mechanics would fall under this definition. Though quantum randomness can produce hard to predict outcomes, those outcomes would have to follow t he laws of quantum mechanics. 

Fair enough. Determinism, as defined by events caused by a prior event(s) dictated by the laws of nature appears to be compatible with quantum randomness (at least from a few minutes of Googling). I was thinking more along the lines of what could be "predeterminism," or the possibility of prediction of future states of the universe based on the past.