Robert,
The videos you are showing are of mostly radar locks on aircraft at very close ranges. Due to this, the visual representation of the lock on the target (in most of these videos, a box "over" it), is jumping around and this is because of the nature of the HUD. Notice that the in these videos, the gun snakes, pippers, and other clutter on the HUD move in this way, they aren't completely smooth. The HUD is not a screen, and therefore indications of radar locks, etc. will not move smoothly (this jerky movement could also be attributed to the fact that the aircraft itself is manoeuvring strongly, leading to buffeting or just general movements that make it more difficult for a projection on a piece of glass to seamlessly track).
The picture from the ATFLIR pod is displayed on one of the DDI's within the aircraft. The DDI is a proper display, not a projection, and therefore of a much better quality than the HUD, therefore leading to smoother elements on the display.
Also, to address the gifs showing the aircraft banking and the target staying stationary, you have to look at the change in bank angle. It is very minor. This tiny adjustment would have a negligible affect on how the target appears initially, and over time this difference would become more apparent.
