This can be a real tricky thing to track down and eliminate
Indeed!
The particular reflection I spoke of is not a hot spot, it's actually a well-focused little chunk of image from outside the normal field, twisted around the optical axis and moved back into the field so as to be visible. Here is an example, carefully constructed to be as obvious as possible:
I cannot tell for sure where in the optical system the problem is occurring. I suspect the prisms in the binocular head.
The problem in this case is not actually due to the camera, it's just that the camera exposes it. Having spotted the problem through the camera, I can now find it by eye as well.
It turns out that due to the internal reflection, the microscope effectively has two apertures: the normal big round one provided by the objective seen on-axis in the usual way, and a second one, smaller, crescent-shaped, and off to one side, provided by the objective seen off-axis via the reflection. At the exit pupil of the eyepiece, these two apertures are well separated. My eye naturally centers on the main one, and the other one is blocked by the iris of my eye. I didn't even know it was there. But the entrance pupil of the camera is bigger and farther back, where the two apertures are not well separated. As a result, when I'm using the camera in this afocal arrangement, it tends to see the reflection that my eye does not.
Interesting, and initially quite puzzling.
Of course now that I know what's causing the problem, I can go about adjusting things to get around it. That's relatively easy in this case.
The type of "hot spot" that you mention can be much less tractable.
Edited to add: The archives of the Yahoo Microscope group are chock full of discussions about concentric rings that appear as if by magic when certain compact digitals are pointed down an eyepiece. Used normally, the cameras work great. Viewed by eye, the microscopes work great. Put the two together and the rings appear. I've been reading carefully for several years, and I have not yet seen a convincing explanation of what causes the rings.
--Rik