When Virtue Device reads prophecy #2214 in Agnes Nutter's book, it says "In December 1980 an Apple will arise no man can eat. Invest thy money in Master Jobbes's machine and good fortune will tend thy days." Later, when various prophecies are appearing on screen as Arizaphale is reading the book, #2214 says "...Master Jobbes's thinking machine".
In showing what should be a page from the book, the type can clearly be seen as either printed by ink jet or laser jet, where a book printed in Agnes' time would be set with movable metal type, which leaves impressions in the paper where the ink pools. These letters are clearly raised from the surface of the paper, with is how ink jets and laser printers work, and do not compress the paper with the individual characters.
Agnes fills her petticoats with roofing nails. In the 1600s, roofing nails did not exist, roof shingles being a relatively modern invention. In addition, nails were handmade and expensive, and would never have been available in a barrel as shown.
The house in Malibu is in a mountainous area that does not match the California coastline as it is too tropical and tree covered.
Gabriel shows a complete lack of knowledge about commerce and how it works - the buying and selling of 'material objects' - in the bookshop. It is later mentioned that angels receive wages for their work. Gabriel would not have been so ignorant in that case.