I had this issue for a while and eventually realized that there were a bunch of .part files in the installer directory.

../Diablo-III-8370-enUS-Installer/

What I had was actually a copy of everything, I had the complete copy of all files but also a bunch of duplicated .part files. The installer would try to use the .part files instead of the actual complete files. Not sure how this happened but I deleted all the incomplete stuff and cleaned up the directory. Once that was done it all worked and installed properly.

Files that should be in the directory
Diablo III Setup.app [folder]
Diablo III Setup
external_resources.rcc
Installer Tome 1.MPQE
Installer Tome 2.MPQE
Installer Tome 3.MPQE
Launcher
SetupOSX.mpq
SetupWin.mpq

Thats it, if you have any other files or folders you can safely delete them. Just in case I am wrong you could move/copy them somewhere else first. However I'm certain this is all I needed to install the game.

I hope this helps someone, Good Luck!