I am trying to copy a photo that I just took with my 1st gen iPad mini (with iOS 8.2) onto my late 2011 MacBookPro (with 10.10.2) and I can't seem to use Airdrop. Is this a restriction of the OS or the hardware and is there any way to overcome it?
No. iOS 8 will Airdrop to and receive from a Yosemite Mac. It is more likely that your iPad (Or Mac) is not compatible with the feature. If your iPad is older then a 4th gen, I think, it won't work.