Two entries with identical name and inode in same directory?
I finally figured out the underlying cause. The following is adapted from my blog post with my findings. 

I connected to the shell of the original server's underlying Linux operating system. I looked at the corresponding directory in the server's underlying file system. This is what I saw (bowlderised for confidentiality and simplified for clarity):

% ls -la /share/Volume/path/to/directory/with/duplicate/entries
total 56
drwxr-xr-x  1 myuser  everyone      4096 Jan  3  2016 ./
drwxr-xr-x  1 myuser  everyone      4096 Aug 24 00:21 ../
drwxr-xr-x  1 myuser  everyone      4096 Aug 24 01:32 .externalToolBuilders/
drwxr-xr-x  1 myuser  everyone      4096 Feb 20  2009 :2eexternalToolBuilders/
-rw-rw-rw-  1 myuser  everyone      4096 Feb 20  2009 other_files


The crucial observation is the directory name, :2eexternalToolBuilders. It begins with the string ":2e", while the other directory entry begins with the string ".". From the point of view of the underlying operating system and file system, there are no duplicate entries in this directory. The two "externalToolBuilder" directories have different names. 

The layers of software on top of the server's operating system — quite probably the netatalk AFP software — interpret the prefix ":2e" as standing for ".". When presenting the underlying directory entry :2eexternalToolBuilders through AFP to my Mac, it rewrites the entry's name to .externalToolBuilders . It fails to notice that there is another entry named .externalToolBuilders in that directory. The result is that my Mac sees, in the original server, a directory with an unexpected, and rule-violating, duplication.

I suspect that the use of prefix ":2e" in place of prefix "." is a convention from old Server Message Block (SMB) file server software.  SMB allowed Mac OS files to be stored on underlying Windows file systems. The Windows file system of the time did not permit filenames with a leading ".". "2e" can be read as a hex ASCII code for period ".". The colon ":" can be read as an escape character, meaning that it plus the following two hex digits should be presented as the character represented by the digits. Thus ":2e" in an underlying directory entry name stands for "." in the directory entry name presented by the server. 

It turns out that the data on the original server was old enough to have been copied forward through multiple versions of server and server software. Sometimes I accessed it through SMB, and other times through AFP. I expect that the directory :2eexternalToolBuilders was created first, and the companion directory .externalToolBuilders was created later. They coexisted, especially for old data which I didn't access. Only when I used Finder to copy the directory did the conflict become apparent.

I speculate that the inconsistent behaviour I saw on my Mac, looking at the volume presented through AFP, is caused by Mac OS utilities treating directory entries differently depending on whether they look up a specific name in a directory, or enumerate all names.  The software no doubt assumed there can be no duplicate names among the entries. Utilities looking for a specific name will find one or other of the duplicates, and stop. There is no reason to look for another of that name, because none should exist. Utilities enumerating all names, or all names matching a wildcard, return all matching entries, not caring that some are duplicates. The duplicate inode number can be explained by the software enumerating all names, then for each name, using that name to look up the inode number corresponding to that name. The software returning inode numbers would of course end its search with the same directory entry both times, because it was looking for the same name both times.

The solution for me was to patrol the underlying filesystem of my original server, looking for cases of duplicates separated by "." and ":2e" prefixes. I found about five cases, with names like .externalToolBuilders, .svn, .libs, and .metadata. I used shell command to merge all files into the entry with the "." prefix, then delete the entry with the ":2e" prefix. This removed the duplication, and let the Finder copy succeed.