Father Brown says the line, "The thing about miracles is that they do happen." This is a line written by G. K. Chesterton, the author of many books including The Father Brown Mysteries.
It is revealed that the Inspector has a wife and two children: an older daughter who appears to be about 14, and a son who appears to be about 10 or 11.
Dean Andrews plays character Michael Negal. You can re-arrange his last name to spell "angel".
Sid Carter (Alex Price) doesn't appear in this Christmas special.