I doubt this issue is related to the Mac Mini specifically.
I have 44 photos shot with an iPhone 3G that will not upload to iCloud Photo Library. I try and drag-and-drop them onto the web interface and I get the same error message you did:
Upload Failed
44 items were not uploaded due to a network error.
However, I have another 62 photos shot with the same iPhone 3G that upload without issue. And I just uploaded 440 photos from an iPhone 4 without issue.
I thought it may have something to do with certain EXIF tags missing on the photos that would not upload but I have not been able to figure out a pattern when comparing photos that work and photos that don't work.
The photos that won't upload open fine in QuickLook, Preview, and Pixelmator so I doubt the image is corrupted in some way.
I can AirDrop the photo to my iOS device and it will upload to iCloud Photo Library, the photo/video count will be incremented on the iOS device and iCloud Photo Library but the photo will never be displayed in iCloud Photo Library. When I delete the photo on the iOS device the photo/video count will decrement on the iOS device but will remain the same in iCloud Photo Library. When this occurred the following error was thrown in the iCloud Photo Library web interface:

Expanding Details shows the following log:
https://gist.github.com/jameswthorne/757e319b9fee63119890