Try the following. It should work.
Remove all traces of Harmony software on the Mac, and do a complete re-install.
Please follow these instructions to remove the Harmony software:
1) Open up a "Finder" window by clicking on the "Finder" icon on your Dock.
2) Select the "Applications" directory.
3) Through the list of the software you have installed, locate the "Logitech Harmony Remote Software" and drag it to the "Trash".
4) Locate another file called "RemoteCore" and drag that in the "Trash" as well.
Once you have removed the Harmony software from the "Application" folder, we would also like you to remove the remote drivers from your computer.
1) On the left side of your "Finder" window, select your "Macintosh HD".
2) Open the "System" folder.
3) Open the "Library" folder.
4) Open the "Extensions" folder.
5) Locate a file called "RemoteControl.USBLAN_usbpart.kext" and "Belcarra.USBLAN_netpart.kext" and drag them to the "Trash".
Once you have removed the USB drivers, it would be best to remove the "Receipt" files to ensure the install goes through without any problems:
1) On the left side of your "Finder" window, select your "Macintosh HD".
2) Open the "Library" folder.
3) Open the "Receipt" folder.
4) Locate the files: "logitech.pkg", "core.pkg", and "RemoteControlUSBKext.pkg". Drag these files to the "Trash".
Once you have removed the Receipts files, you need to remove the "Logitech" folder found in your "Users" Home directory.
1) On the left side of your "Finder" window, select your "Macintosh HD".
2) Open the "Users" folder.
1) Select your "Users" home Folder (picture of a house).
2) In you Home directory locate the "Logitech" folder and/or "browser - Logitech" folder.Drag these to the "Trash".
Once you have completely removed these files, please go ahead and installed the Harmony software 7.4 located in the link below:
http://www.logitech.com/index.cfm/410/&cl=us,en?prodcrid=410