The width of the street that the car gets stuck in.
Nick jumps in a scull and joins a race. Near the end of the race, from an overhead shot, he is seen tied for first place with another scull. The scene then changes to a closeup of Nick with the other sculler far ahead to his left. (That footage was repeated from an earlier scene in the race). The scene then changes again to show him winning the race.
When Nick shows up dressed per the invitation, he is let in through the "dog room". As they walk in, that inside door is left open. He's inside about 2-3 minutes until he realizes what's up and then starts to sneak out, but now the dog room is full with the inner door closed. Who did this, and when? Those dogs weren't around anywhere before then.
When Nick is first invited to the party by Victoria, we see her with a glass in her hand. Soon he grabs two wine glasses from a server's tray, and goes to hand her one, and her hands are empty. Then they walk out of the room and seconds later, in the next room, they don't have the wine glasses so he pours them both a drink.
During the "Matriculation Ceremony", students/extras are seen wearing the undergraduate academic dress, and most are wearing their mortarboards. However, undergraduates at Oxford do not wear their mortarboards on their heads, but instead carry them, as they are not yet holders of their degrees.
There is no architecture course at Oxford.
Sconcing is banned in Oxford and certainly would not be done in formal hall with all the fellows of the college looking on.
Virtually no one has a roommate at Oxford.
When students are leaving the "Matriculation Ceremony", some are wearing carnations in white, pink, and red. These are traditionally worn for Oxford examinations, and never at any other time.
When the sports car is being lifted by the crane at the docks, you can clearly see the front wings are a different shade of red to the rest of the car. This indicates early on in the film that it's going to be crashed / damaged in those areas.
When Nick asks the man in the Mini for directions to Oriel College, the street name "Oriel Passage" is clearly visible behind the cars, and so Lowe would be looking straight at the front gates, which are across the road.
The reflection of the equipment is visible through the revolving door as the Las Vegas Lady enters the casino after saying goodbye to Nick.
Complete mixup of Oxford geography.
Professor Boggs quotes Casablanca to Nick, saying, "In the words of the inimitable Claude Rains... 'I believe this is the beginning of a beautiful friendship.'" In actuality, that was Humphrey Bogart's line, not Rains'.
In the final race the oar gate opens and they lose valuable seconds getting the oar back in, at which point the Harvard team is several lengths ahead. So, the Oxford team catches up and passes the Harvard team, but if that happened, the pace they were on should have put them well ahead of Harvard yet we see them at almost the same pace at the finish line. Harvard crew didn't wait for them - they would have stayed on their pace.