Well, the easiest way to point out that it's wrong is the fact that all the planets orbiting our sun are on the same elliptic plane as the galaxy. Not perpendicular as the video shows it. That's the point where you can stop the video and dismiss it entirely.
Sorry, but that's not right. The ecliptic plane (the plane in which the Earth orbits the Sun) is tilted at 60.2 degrees relative to the galactic plane. It's closer to perpendicular than parallel.
The video is basically right about its facts, but completely wrong in how it interprets them. The key is to understand that all motion is relative, and how the motion of an object is perceived depends on what frame of reference you're observing it from. For instance: Imagine you're sitting on a moving train, playing with a yo-yo. From your perspective, it looks like the yo-yo is moving straight up and down, because you're defining your coordinate system relative to the train itself. But to an outside observer standing in the station and watching the train go by, it looks like the yo-yo is moving in a sine-like wave, not just moving up and down but moving sideways. That's because that observer is defining her coordinate system relative to the station, which isn't moving with the train. Which one is right? Both of them are! It all depends on how you're measuring it. There is no frame of reference that's more right than another.
This is the exact same situation. If you're standing still relative to the Sun and watching the planets go around it, you see them following elliptical paths. But if you're in a different coordinate system, say, one that's motionless relative to a distant galaxy, then you see the Sun moving in its orbit around the center of our galaxy and the planets moving around it at roughly 60-degree angles (since the different planets are all in slightly different orbital planes, not perfectly in the Earth's ecliptic). So if you drew out their paths in that frame of reference, they would be lopsided helices (not spirals, since a spiral is a path that increases in radius as it goes around; a helix is more like a Slinky, maintaining its radius but changing position perpendicular to that, or nearly so).
But this is a trivial distinction, because both are equally correct ways of defining the motion. The only difference is in what coordinate system you're using. And changing the coordinate system does not invalidate the underlying physics. The planets are still being drawn toward the Sun by its gravity, and the combination of that attraction and their momentum produces the paths we observe. You get that same result regardless of which coordinate system you use and how you define their motion. It's just that choosing a coordinate system that treats the Sun as motionless is the simplest way to solve the equation, because that way you get to ignore terms (like the effect of the galaxy's gravity on both the Sun and its planets) that would cancel out of the equation anyway and don't make any difference to the result.
So this video makes a common mistake of a lot of Internet charlatans -- taking some scientific facts that are basically correct in isolation, yet completely failing to understand how to interpret their meaning.