When discussing Columbus' journey John implies that there was still widespread belief that the earth was flat. In fact, since the time of the Greeks it had been relatively common (educated) knowledge that the earth was round. (Columbus' error was in underestimating the diameter of the earth and thus the distance to Asia by a westerly route. Luckily, he bumped into the Americas where he'd roughly calculated Asia was supposed to be, otherwise they'd have been lost at sea.)
At about 15 min in, one of the scientists talks about Britain becoming separated from France when the glaciers melted. The biologist says with surprise, "That happened?" Anyone with a doctorate in biology would know that.
After Dan questions Dr. Oldman about keeping relics, Dr. Oldman walks out of the house carrying a box, and Sandy follows him also carrying a box. When the camera angle switches to an outside shot, they've changed positions: Sandy comes out first followed by Dr. Oldman.
When John invites his friends into the house, he tells them the electricity is on and the gas is off. Later, the fireplace can be clearly seen to be a gas fire (the flame is coming from the bottom of the fireplace, not from the logs).
When Dr. Grubber first arrives at the house he sits on the couch and begins asking John questions. Dr. Grubber's arm position alternates with the different camera shots from resting on the couch's arm being tucked in at his side (off the arm of the couch). Edith's position can be observed to be different between these shots as well.
It the very beginning of the movie, Edith (Ellen Crawford) notices a painting on the ground by the truck and asks about the artist. The dialogue makes it clear she saw the painted surface of the canvas but she wouldn't have been able to see it from it's angle and from where she was standing.
At the beginning of the movie when Oldman is loading his truck and his friends arrive, one of them asks to help with a heavy box. They both lift the box on the truck bed and then Oldman pushes it on his own further.