Answer: Artifacts. But what produced the artifacts???
Artifact: something observed in a scientific investigation or experiment that is not naturally present but occurs as a result of the preparative or investigative procedure.
Object space is the 3 dimensional space in which a graphic object is defined.
Image space is the projection of the object into two dimensional screen space.
This mystery dot problem is similar to a UFO image. We are presented an image without an obvious explanation for its appearance. Is this an object or an artifact? Or something in between, like a rainbow, which is created in object space but has no physical location in that object space?
There are three moving dot images in the video between the 3:40 and 3:50 timestamps. The one specified by the OP corresponds to the yellow track in the frame below. I have transposed the tracks to an earlier frame (1:12) to provide clearer contrast with the spacecraft structure and the moonscape in the background.
The short blue arrow corresponds to an image track which spans from the last exposed frame into the blank overexposed frames which follow. Below is one of the overexposed blank frames:
Since this moving dot image persists after filming, it clearly does not originate in object space. So we have proof that this optical system is capable of producing dot-like artifacts which move diagonally.
However, just because the system is capable of producing compatible artifacts does not necessarily mean the other dot-like images are also artifacts.
The longest track (yellow in the illustration above) appears to come into view from behind the spacecraft and disappear behind the strut. This supports the conjecture that the image originates in object space beyond the structure of the spacecraft.
However, the moving dot does not reflect from the mirror panel adjacent to the position where it first appears. The mirror finish on this area is not apparent on freeze-frames, but is convincing when viewing the video from 1:28 to 1:50. Multiple craters are reflected as they pass this triangular panel. As an example, here is a detail from 1:43. The blue triangle is the mirror panel. The yellow area is the crater shadow and the green semi-circle is the shadow’s specular reflection in the mirror panel.
For comparison, here is a similar view of the dot-like image as it first appears in the same location. There is no specular reflection, despite perfect contrast conditions.
This appearance is consistent with an artifact, rather than an object in object space.
I don’t have proof these moving dots are artifacts and I cannot offer a mechanism for such artifacts to form. But I think, on the balance of evidence, they should be considered artifacts rather than objects (until more evidence is available).
While viewing many, many frames from this video, I saw many dots about this size and brightness. Some were present for a single frame. Some were present for several frames, often giving the appearance of movement. A single dot could be explained by a cosmic ray, but not serial dots in analogous positions on subsequent frames. Very puzzling.