As is said at about 13:03 it's "very hard to adjust" the camera and binoculars to see the extra objects.
Now if these were real things in the sky you should just be able to point the camera up there and see it, right? There's no adjusting needed to see the white moon.
Why would you have to find the exact angle between the camera and binoculars to see the other things? Well, simply because the light has to hit the lenses in the right way for the reflection to appear.
At the beginning of the video the blue moon is really close to the real (white) one.
Then all of a sudden it's dropped down the equivalence of its entire diameter :
So what happened in those 25 seconds?
There was a switch in which one of the binocular eyes the camera's looking through.
If the object was really behind the moon those 2 inches (or something) wouldn't make it move a bit. But the viewing angle has changed and so does the reflection.
If you're good at angular mathematics you can probably prove that those inches fit the diameter drop perfectly.
At the end we can see the upper brownish reflection shake with every small movement of the camera, once again proving that the object is caused by something in the camera.
