@Dubdrifter , I am an astronomer who will take take some time to explain what I think is going on. I specialise in the Milky Way and nearby galaxies, not Solar astronomy, but I don't think that is important here. More relevant is that I worked for 8 years at the Space Telescope Science Institute in Baltimore, have therefore experience with the Hubble Space Telescope and also other space mission data, as well as a lot of ground based astronomical data. I now have a permanent position in Germany, so have nothing to do with NASA anymore (and actually, the Space Telescope Science Institute was set up to be independent of NASA, so that decisions regarding Hubble can be based on science interests, not on political or managerial interests).
If you look at the left side of the window in the video in the panel marked "image", you can see that the data shown is from the UEVI detector of the SECCHI instrument in the STEREO-B mission. Just above that information you see the time stamp of the data in green. It turns out that the data available comes in steps of 10 minutes, not 1 second as suggested in the video. This is not uncommon; this has nothing to do with how fast the camera can take pictures, but with the data rate they can be sent back to Earth. You should think at rates not much faster than your analog telephone line modem if you are old enough to remember that. Design of this satellite was probably started about 20 years ago and may have technology on board that is even older. For instance, this camera runs on a PowerPC chip that older Mac lovers will well remember.
So even though the top level time selection is shifted by only one second, in reality an image taken 10 minutes later is shown. The display just shows the image taken closest in time compared to the time selected in the top panel, so shifting from the image taken 5 minutes earlier to the image taken 5 minutes after the time selected by moving just 1 second in selection.
And indeed, the Sun changes that much in 10 minutes in terms of solar flares, not in 1 second (that would probably be faster than light given the enormous distances covered). The bright specks are most probably what astronomers cal "cosmic ray events", charged particles that shoot with high speed through the detector during the exposure, discharging a lot of electrons that are read out and show up in the image as bright spots. The design document of this instrument states that they expect about a 1000 pixels affected by these events (out of 4 million pixels) in each exposure. Because we don't see that many this probably means that most of them have been removed by an automatic software detection algorithm, but this is hard to do perfectly especially on the smaller, fainter events, which means that some faint spots may still be in these images.
So the bottom line is that images are compared that were taken 10 minutes apart and have some of these faint cosmic ray events at different places in the image (have a careful look and you see others in the other images). The Sun had a small outburst in one of these images (releasing many new charged particles in the process!), but this had absolutely nothing to do with the change in position of the spots.
I hope this answers your question.
And regarding astronomers not often answering these kind of questions: the internet is so full of these kind of questions, that it is almost impossible to start. We do in general our best to answer question directed directly at us at our outreach departments (and as discussed above, almost every astronomy department has someone responsible for outreach). We could spend easily our full day on answering questions on the internet, but we rather do research and discover new things. As mentioned earlier in this discussion, scientists have no interest in hiding things from the public as often suggested in conspiracy theories. Scientists are just curious people, looking for the "truth" (whatever that is), where it is in their interest to their career to discover new things, not to hide them. But more importantly, one of the most important commodities they have is integrity. If other scientists suspect you are not trustworthy, your career is in serious danger. Therefore, scientists may make occasional mistakes like anyone, but deliberately giving wrong information will be rare. As others will be building their science on your results, the chance that you get caught out for cheating is just too big and the truth will come out eventually, especially for high visibility results.
