a space in the filename

That should not really cause trouble but not only for SEO I would recommend to avoid spaces and any special chars in file names. Zenphoto would try to clear on upload but the seo_zenphoto plugin must be enabled for that. FTP upload bypasses that naturally but the seo_cleanup plugin can clear file/folder names afterwards.

Another common issue is wrong file/folder permissions the can cause all sorts of issues.

Thanks for the tips
I checked a small sample of the files that result in {{ERROR}} and they have Color space RGB and Color profile uRGB and Alfa channel No but so do many of the other photos that present just fine.

There is nothing in the Debug log - in fact it is not even created on the new installs (which I understand is normal if there is nothing to log).

Is there a Debug plugin to manage the various debug flags or is there somewhere to enable them manually?
If so where and which do you suggest?

I have copied the zp install to MAMP and that file is always displayed correctly there.

I have copied the file to another directory on the same shared hosting server and the image displayed correctly the first time I displayed it. (I note that the action of displaying it caused a symlink to be generated and it always displays {{ERROR}} afterwards.

You don't need to enable the debug log. If there is anything to log it will appear in the debug log.

Early/deep PHP server related errors will only be in the server side PHP error log as they happen before anything of ours gets executed. You have to ask your host if you can enable and/or where review that (a good idea to know in any case).

You can also enable several debug modes for extra info for ZP related things via the config file:
https://www.zenphoto.org/news/debugging/

I can only assume that symlinks may not be working correctly on your server although it say they do. Check the permissions of the files maybe.

For sure something on my host server symlinks is not working as expected.

I copied the directory that had image files that were giving me grief.

I copied the files that were a problem and renamed them without spaces or '(' or ')' (by default my mac renamed images that had the same sequence number with a space and (sequence number) e.g. photo (2).jpg. And I left the "badly" names files there.

After uploading that album and cache to my test copy on the host server I can see that the "poorly" named files still fail while the well named files, use - and not space, underscore or ( or ) then all seems to work for those files.

I can only assume that symlinks may not be working correctly on >your server although it say they do. Check the permissions of the >files maybe.
Once again - You are correct!

It is enough to know the rules not so important to me to know why it doesn't work (though I think it is clearly a difference caused by the host server implementation or configuration of symlinks).

Let me try renaming all the image files giving me grief and see if the {{ERROR}} problem goes away for good.

FYI the permissions of the files
thumbs - 644
symlink - 777
album directory - 755

I also tried all combinations of the 2 settings for Options > Image > Full image protection and none appeared to make a difference.