Most often this is caused by access permissions not being stored correctly on the device’s file system. Please tell us what operating systems and file systems are involved. Or just try out the “Ignore Permissions” advanced folder option.
And do have a look at the list of items that are affected. It may point to some common problem like forbidden file names.
I understand what you said, but I’ve been using Synching for several years with no problem until I incorporated a new computer to my home network and then an existing computer suddenly started reporting that it was “Out of Sync”.
Trying to determine the steps needed to be performed to resolve the issue.
Well it’s hard to debug this with rather little information. What is the real situation with the listed paths? Do they exist at all? On which devices? On which not? Have they existed in the past?
The error message about the out of sync items is rather clear: There is a directory with files in it that Syncthing doesn’t have in its database (only reason for that I can see is that they are ignored). That directory was removed on some remote device. The Syncthing instance that’s complaining about it sees a non-empty directory which it will cautiously avoid to delete unless it has itself deleted any files in there.
Sorry this is going a bit slowly, but I just don’t get a good enough picture of the situation yet to pinpoint what is wrong.