How to check which files have been copied to the main hard drive and which ones have not been copied?
From my experience I may recommend Path Finder app (http://www.cocoatech.com/pathfinder/).

It has very powerful Commands -&gt; Folder Sync command that does exactly what you are asking for: shows synced files and those you may need to copy left or right. They are highlighted with different color.
App has free trial period (fully functional) and then asks for some money, but it's totally worth the price.



Red arrows just show some random directories. You can select your own, including those on different volumes. And you can compare file content is required.