When Hawking's mother tells him he has a phone call from a woman, it cuts to Jane waiting on the phone. There is then a 'hang up' click followed by a dial tone. This would not have happened with the pulse-dial phones in use in the UK at the time (and until well into the 1980s) because only the caller could properly terminate a call and free up the line. Jane may have heard a click, but not the dial tone, since the line was still open until she hung up.
When Steven Hawking's life is played backwards and rewinds later in the movie, the sequence of his collapse and tracheotomy are the wrong way around. It should show him having the operation, then winding back to his collapse in the Wagner concert, but the incidents are in the wrong reverse order.
When Stephen is at a summit after the release of his book, he sees a young lady drop her pen. In his imagination he leaves his wheelchair to pick it up for her. In the wide shots he is picking it up with his right hand, but in the close-up he is picking it up with his left hand.
(at around 49 mins) After Stephen gets the knitted sweater stuck over his head, he tells Jane he's had an idea. Jane then pulls the the sweater over his shoulders, but in the next shot it is once again hanging from his neck.
When Jane is talking to Stephen on the phone in his dorm room there is a ring on her left ring finger. While playing croquet the ring is on her right hand ring finger and later it disappears altogether, until after the wedding.
The first shot of a chartered plane shows an aircraft with one turboprop engine on each wing. The background audio is, appropriately, the sound of a turboprop engine. The next angle shows a wing with a joined pair of turbo jet - NOT turboprop - engines. Different planes.
During the May ball, the constellations Sagittarius and Scorpius can be seen in the night sky. From the latitude of Cambridge, England, it is however impossible to see these constellations at this height above the horizon.
When Hawking catches a train to London, he struggles up the stairs from the subway at the station. There is only one platform at Cambridge Railway station and consequently no subway or footbridge. The actual location is Horsted Keynes in Sussex.
As a student Hawking is shown a lab in Cambridge and told that was where Rutherford was the first person to split the atom. This was achieved when Rutherford was chair of Physics at the University of Manchester.
When the rest of the family is traveling to Bordeaux by car they are traveling in a Volvo 740 (745) station wagon. It's stated in the movie that the youngest child, Timothy, is only a baby. This could not be as Timothy Hawking is born in 1979 and the Volvo 740 went into production in 1984.
Sciami asserts that Rutherford "split" the atom. That is a newspaper cliché explanation that no scientist of any discipline would say, but "brilliant deduction of the structure of the atom", might not sound so catchy.
When Jane visits Stephen in the care home the residents are watching an episode of Countdown clearly showing Carol Vorderman in the '80s or early-'90s. The clock on the wall shows 3:10 however in those days Countdown was only aired after 4pm.
When Hawking is explaining what is wrong with him he describes it as Lou Gehrig's disease. This term was almost unheard of in the UK at that time and certainly would not have been used. He would have described his diagnosis as ALS. The term Lou Gehrig's disease was probably included for US audiences.
When Jane Hawking is attempting to teach Stephen how to speak using eye cues, after his tracheotomy surgery, she states all of the colors on the board except yellow. She does this twice in spite of the fact that yellow is clearly visible.
(at around 25 mins) The doctor tells Stephen that he has motor neurone disease "that destroys the cells in the brain - that control motor function -." At 26 minutes, the doctor says "the brain isn't affected."
Actually, the disease destroys motor neurons in the brainstem and spinal cord, but not in the cerebrum.