If we have adoption expenses (from 2015) for an adoption that was finalized in 2016, can we apply for the 13,460 credit?

Yes, the adoption credit can be claimed for expenses paid in the year they were paid OR the year the adoption was finalized.  As long as you did not already claim them, add them for 2016.  Congrats!

For some reason the system won't let me get the credit... Have you heard of any issues with the system?