Q To provide extra safety, I tried copying my iPhoto Libraries to my NAS drive, but that failed. How should I back these up, given that one resides on my MacBook, and the other on an external hard drive?
A Generally iPhoto, Aperture, and Photos Libraries are best backed up using Time Machine.
These libraries look like single files, but are actually folders containing thousands of files in an elaborate hierarchy of hundreds of different folders. Time Machine minimises redundancy in backups by copying across only those components which have changed since the last backup, whilst making a simple Finder copy will create another copy of every single file within the library, each time.
Network-Accessible Storage (NAS) storage systems from third parties emulate the Mac’s normal file system, which may not always cope properly with the elaborate structure of these libraries (or with Time Machine backups).
It is also possible that your library has a problem with it, and needs to be rebuilt by iPhoto: see this article for details.
Third party apps like Folder Sync can sometimes help with external libraries which cannot be backed up using Time Machine.
Updated from the original, which was first published in MacUser volume 29 issue 11, 2013.