I posted a message in Apple Support : In photos I’m getting the “Error downloading slideshow photos” even though I don’t keep any photos on iCloud.
However, I stumbled on a workaround myself and thought it might be useful to others:
I began by selecting a few images at a time and clicking on Slideshow, then I cut down the number until I found one that was causing a problem. Then I tried to find a copy on my computer to see if I could replace it. However I didn’t find one so that avenue was a dead end. Next, and I’m not sure why, I selected revert to original with the problem photo and lo and behold slideshow worked. So then I did undo revert to original and Slideshow still worked.
So as a final test I took a whole folder reverted to original and then undid revert to original and Slideshow worked.
Of course this doesn’t explain what the original problem was but hopefully this will help people with the same problem or perhaps Apple Dudes to improve the Photos App.