I didn't realize the sun oscillated up and down through the galactic plane. That's neat. 
That part is one of the few things more or less correct in the vid (though he gets the frequency wrong). All this looks like somebody who's not good with physics thinking he understood how the sun actually moves. It looks to me that he's trying to use simplified, "popular science" explanations like actual science. That reminds me of proving 1=0 by abusing rounding definitions.
Also, the argument that heliocentrism is wrong is a funny case. Putting aside bad science, he seems to be equating "wrong" with "noninertial". The "correct" (i.e. actually inertial) system (using that definition of "wrong") would take the universe itself as a reference frame. Calculating the motion of a thrown ball in such reference frame would yield a mindboggingly complex equation. Once again, too many oversimplifications lead to a wrong conclusion. Noninertial frames are perfectly valid and usable (indeed, this perfect inertial one is pretty much useless because of it's complexity). Eg. when considering a ball on Earth, it's perfectly safe to assume a geocentric reference frame is an inertial one, because influences from the moon, sun, galaxy and all that are pretty much meaningless. Aside from a
very bad case of OCD, I see no reason to include them in such a case.

Choosing a correct reference frame can greatly simplify complex problems, and there's no frame that is "wrong".