Anathema has an index card with the prophecy of her encounter with Newt. Wide shots of the index card show hand-written annotations at the top of the card, referring to a Japanese car. Those annotations are changed in subsequent close-up shots of the card.
When Anathema and Newton are kissing under the bed, the wide shot shows the bed spinning above them, but the close up shows the wire framing on the underside of the bed as stationary.
The Captain of the cruise ship has his rank epaulets on back to front, the ribbon should start from the front and the loop folds over the top, not the other way round as shown.
The Captain of the Morbilo says they were proceeding south-southwest on course to Havana when they ran aground on the lost continent of Atlantis. Later in the show Crowley's globe shows Atlantis off the southeast coast of Brazil. Going to Cuba from there would require circling South America and going through the Panama Canal. Or taking the long way around the entire southern hemisphere.
Lower Tadfield is supposed to be in Oxfordshire, yet Shadwell's map shows rural Buckinghamshire, just outside Marlow.
Newton says "You don't get tornadoes in England." This is not strictly true. England gets more tornadoes per square mile than the USA, but they are minor tornadoes, almost all F0 or F1 (wind speed maximum 110 mph).
Anathema tells Newton that Agnes Nutter was a witch from 300 years ago. A minute later she tells him her family has been trying to figure out Agnes's Nice and Accurate Prophecies for 400 years.