When David has a drink for "Dutch courage" in his car he takes the wrapper off the bottle of wine and then makes another movement like unscrewing the cap. Screw tops weren't found on bottles of wine in the 1960s.
When Jenny finally passes her A levels, she mentions grades. The film is set in 1961 - A level grades were first introduced in 1963. Although,when she's studying at home, it is implied that a significant amount of time passes, it is unlikely to have taken her beyond 1962 when, essentially, you either passed or failed GCE exams.
St John's, Smith Square, was bombed in 1941; it's restoration didn't commence until 1965 and was completed in 1969. It didn't, therefore, become a concert venue until nearly a decade after the time at which the film was set.
In the Youth Orchestra scene, the orchestra are playing Elgar's so-called Third Symphony. At the time that the film is set, this Symphony had never been played and simply existed as sketches which were unfinished at Elgar's death. It was not until 1998 that the composer Anthony Payne edited the sketches and enabled the Symphony to be premiered.
In the scene where David is showing the Caribbean family to their new flat, a car can be seen in the background going over a speed hump (or sleeping policeman). These traffic calming measures weren't introduced to the UK until the 1970s.
Danny and David are shown on front seats of the car when Danny tells David that he has seen a For Sale sign. In the next scene the car pulls up to the house for sale and David and Jenny exit from the front doors.
When David places Jenny's cello in to his car in the rain storm he places it in headstock first from the passenger side, putting the headstock on the driver's side. When they arrive at Jenny's house, she comes to the driver's side and pulls the cello out bottom first. The cello turned 180 degrees during their drive.
When Jenny was walking home and met David for the first time, she was walking beside the car while he drove. There was a shot of him speaking to her and it showed a dry car, no rain and windshield wipers moving on a dry windshield.
When Jenny is taking the bus (apparently to Ms. Stubbs flat) it is night and raining; when she walks into the flat, sun is pouring through the kitchen window and birds are singing. In the next scene, she is riding in a bus at night and in the rain.
In the dog track parking lot, David takes a few things out of the back of his car and sets them on the ground. Although they are seen there throughout the scene, they are suddenly gone when he and Jenny leave even though he is never seen putting them back.
In the scene where Jenny is showing her parents the book with the fake inscription, her father grabs back the book right after he shows it to his wife, and the camera switches off to Jenny. Then, when it switches back to her father both the book and his glasses are gone.
In the scene where Jenny receives two dictionaries, the top dictionary is still wrapped when her father answers the door to greet David. The scene is continuous, however once David appears near the table with his presents, both dictionaries are now unwrapped on top of each other on the table.
In the final scene Jenny and her friend can be seen cycling into the Bodleian library courtyard. Bikes are not allowed in the Bodleian and others can be seen chained to the railings outside. There are also 3 steps up to this courtyard which they would not have been able to cycle up.
At the end, when Jenny is admitted into Oxford, she receives a letter from the University ("faculty of arts"). In fact, students are admitted into a specific college, and her admission letter would have come from the college, not the university.
When Jenny invites David to the concert, she indicates that the composer is Elgar. David replies, "I'm afraid Elgar and the Jews don't get along". This may imply either Jews don't like Elgar (hard to prove) or that Elgar was anti-Semitic.
However there is no evidence of Elgar being anti-semitic, in fact from Elgar's biography - "1933 Flies to Paris to conduct performance of the Violin Concerto with Yehudi Menuhin (with whom he recorded it the previous year); visits the paralyzed Delius; writes of his dismay at Hitler's anti-Semitic policies in Germany;".
This does not appear to be an error - it is simply Goldman's opinion of Elgar, perhaps formed by Jewish acquaintances who do not like Elgar.
When David leaves Jenny's house after failing to admit his guilt to her parents, you see headlights passing the house twice. Being parked on the curb next to the house, if he truly had to turn around, the headlights would reflect away (not toward) the house.
When Jenny is in her room crying after finding out about David, her father is talking to her behind her room's closed door and says "there's a cup of tea & some Biscuits out here" but if you look closely into the cup it's not tea it's most probably coffee or Chocolate Milk.