Plot hole: George is standing in the small park across from Filby's department store when an atomic weapon detonates. The cars in the street are instantly turned into burned hulks and the building crumbles and bursts into flame. However, George, standing no more than 20 feet away from both, doesn't even break a sweat! While shock waves from a blast can cancel each other out and leave things unhurt, the sheer thermal energy released should have severely burned him at the least.
Continuity mistake: When George stops his time machine at 802701 A.D. he stops it too fast and falls out of his time machine. While he's lying on the ground rain falls out of the sky and only lands on him and a little bit of the ground. When George stands up however his hair and his clothes are completely dry and steam is rising from the ground.
Continuity mistake: In the scene when George and Weena are collecting wood for a fire outside the Morlock's entrance George throws a pile of sticks to where Weena is sitting. One of these lands precisely between her legs, in the next shot the stick has gone.
Other mistake: When the land is getting destroyed by the volcano, George is in his time machine and the disc attached to it is already spinning before he even turns on the machine and throws the lever forward.
Factual error: When George starts time traveling in his lab, we see the sun and moon cross his field of view. But then we see stars circling Polaris in the same area. Polaris is nowhere near the path of the sun.
Continuity mistake: When the Time Traveller gets back into the machine after the volcano scene, because the numbers are turning so fast, you can only see the first number; the first time you see this, the first number says 8, then 9, indicating 8,000 then 9,000 years, then it cuts to the Traveller for a second, and when it is seen again, it says 8,000 then 9,000 then 10,000.
Continuity mistake: When Alan Young and Rod Taylor are talking outside of Filby's Department Store during World War 1, the curtains in the windows can be seen blowing in the wind because there is no glass in the frames.
Other mistake: When George climbs into the Time Machine for its test run, he becomes fascinated with the changing fashions of a mannequin in a store window across the street. As he watches the mannequin, the days and nights are flashing by, as indicated by the studio set lights changing from white light to blue light, and by the exterior lights of the building, which switch on at night and off in the day. At first, the shopkeeper appears in the window, also, changing each costume on the mannequin one-by-one. As the shopkeeper labors to change a single costume, the exterior day/night lighting changes three or four times, indicating that the shopkeeper improbably spent three or four days, working day and night, to change just one costume.
Chosen answer: It is specifically not stated which three books he took with him, leaving it open to audience speculation.
Mobrien316