For a scientist, Dr. Markway exhibits an astonishing lack of scientific curiosity regarding the "Help Eleanor Come Home" writing on the wall they discover. He tells Luke to wipe it off the wall, without even taking photographs of the writing or samples of the chalk-like substance used to write it.
Look closely at Dr. Markway as he folds his paper at the breakfast table and you can see he is holding a cigarette in his left hand. In the very next shot, Markway is holding the cigarette in his right hand instead.
When Nell is leaving the Garage in Boston, she sees a signpost that is, for the most part correct with respect to route numbers and directions for the towns indicated. However, one sign refers to "US 50" and Nell then reads aloud her directions to take "US 50 from Boston and watch for the turn-off to Route 238." US 50 is nowhere near Boston; prior to the advent of the Interstate system of highways, US Route 50 was one of the principal highways that went straight through the middle of the country from Maryland on the East coast to California on the west coast.
When Eleanor runs into a room in Hill House, a close-up shot shows a mirror fall off a mantle on its own. However, a wire is visible attached to the middle of the back of the mirror and going through a hole in the middle of the wall behind it. When the mirror falls, the wire goes slack as the wire feeds out of the hole in the wall, meaning the wire was held taut to hold the mirror up on the mantle until it was time to release the wire.