When I was a research physicist I spent a lot of time looking at the effects of ionizing radiation in pictures, although mostly in the context of digital images. The mechanisms are a bit different for photo emulsions, but to me the reason I'd discount radiation is because they're specifically filtering for features that exhibit the expected point spread function (which is a geometric property of the telescope's optical assembly itself). I guess you could test by exposing emulsion plates to ionizing radiation and seeing how often you get PSF-like images by chance. Also, their search is for +/- 1 day of nuclear testing, which seems weird. Certainly radiation from fallout wouldn't make sense on the day before testing. It would have been useful to see +1 day and -1 day separately. Or 0-2 days. The way it's chosen makes me suspect they couldn't find a signal in those windows, and therefore it's probably just statistical noise that they've massaged out of the data.
But to me the biggest flag is that these images are from 50 minute exposures. The objects don't appear as streaks, so they are either very, very short flashes (much shorter than 50 min), or they are very far away. The authors interpret this to mean the objects should be in geosynchronous orbit, which doesn't make sense; objects in geosync would still appear to move relative to the star background over the course of 50 min. Yet this is the entire basis for their "shadow deficit" window calculation. You could constrain the duration vs distance by looking at the effect it would have on smearing the PSF, which would be interesting.
Overall it seems pretty unscientific. If you go looking through enough statistically noisy data for signals in enough places, you'll eventually find it.
> The objects don't appear as streaks, so they are either very, very short flashes (much shorter than 50 min), or they are very far away.
Couldn’t be aberrations in equipment, like lenses? Or film development?
Yes, 50-minute exposures would certainly rule out geosynchronous; I've used image stacking to look at geo and you get visible movement relative to the star background after even a few seconds. Fifty minutes would be almost 15 degrees of movement relative to the background! This isn't even accounting for the fact that you would need to be looking in a narrow region above above the equator to get something geosynchronous to begin with.
There are other possiblities that are likely: Upper atmosphere tests resulting in transient luminous phenomena. This would be more likey in certain conditions where the sun could reflect off of specular matter (e.g., bits of metal). You would see this most likely within 1-2 hours of sunset or 1-2 hours of sunrise (source: I've used optical equipment to spot satellites professionally).
I'd note that thier pipeline for removing "plate defects" is not based on the PSF but on some vaguely defined "expert review" training. This can, and should, be a quantifiable step.