These contentions are supported by a variety of telescope and SOHO imager artefacts, and a poor understanding of what planets look like through a telescope.
A prime example is here. Now Dave Greg has dealt extensively with the telescope appearance imager artefact side of things (see here, here and here).
But there is one area where I feel the need for a bit more comment. The video says it will show you shocking evidence that Jupiter has moved from the ecliptic. The images above are a series of images from SOHO, where the position of Jupiter in the SOHO imager has changed. In the images above I've shown the same SOHO images as are in the video, and Jupiters position is different with respect to the central occulting disk. The fourth image is an overlya of the previous three to show the changes clearly.
"Why Hasn't Astronomy Pointed out Disturbed Orbits?" asks the video after the SOHO images.Because the orbits aren't disturbed. Jupiter is exactly where we expect it to be, because Jupiter's orbit is not exactly on the plane of the ecliptic, but at an angle to it.
Jupiter's orbit is inclined to the plane of the ecliptci by one degree. This may not sound much, but it is twice the apparent diameter of the Sun (and Moon), thus in its orbit, Jupiter can move (from earth's perspective), substantially above and below the ecliptic. The black and white charts above (click to embiggen for a better view) shows the predicted position of Jupiter at the same dates as in the SOHO images as seem from Earth.
As with the SOHO images, the fourth image is an overlay of the previous three to show the changes clearly. The central black line is the plane of the ecliptic and the big circle the Sun. Jupiter is labelled. Note that in the SOHO images the occulting disk is bigger than the Sun, so in image one in the SOHO series the occulting disk touches Mercury,
They are almost identical to that of SOHO, but aren't exactly the same as SOHO is in a halo orbit around Lagrange point 1, and has a slightly different point of view to that of Earth. Nonetheless, the charts show that the amount of movement we see in the SOHO images is what we expect of Jupiter's orbit.
Note that the software I am using is from 2005, using a 1989 model of the planets orbits, which has not been updated. Thus the agreement between the plotted positions and the observed positions is not due to post facto orbit tweaking.
Planetary orbits have not been disturbed, the planets positions are exactly where we expect them to be. It is hard to tell if the posters of these claims, like the poster of the video we have been discussion, are merely deeply clueless about astronomy, or are deliberately trying to wind people up.
In the meantime, the next tie someone posts a video or claim that the planets orbits are disturbed, ask yourself "how would hundreds of thousands of amateur astronomers not notice this?" and contavt your local planetarium if you are worried.