No Thumbnail?
 

I have the gallery set to see the most recent photos. If I click on one of those photos and move it to another category, when you go back to the main gallery, it shows No Thumbnail in the most recent photos. Why is that happening and can I correct it?

What version of the software are you using?

Sorry...5.62

What happens if you try it after turning off the category cache in admin => global options

No change actually.

However, I did notice that they all change back to a photo at some point. I've tried logging out and back in to see if that triggers it...and I've tried to time it...but it's all random. But eventually, they change back. ??

Try turning off your category cache and set the minutes that it updates to 0 and then try