These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Danny: [about David] I'd be careful if I were you, Jenny. You don't know who you're dealing with.
Moral Event Horizon: David runs out on Jenny after she discovers he's married instead of helping her face her parents and telling them the truth of his deceit. To make matters worse, Jenny is unable to return to her school (and therefore cannot get into Oxford), and has basically lost almost everything because of David—or rather, because of herself.
Spell My Name with an S: Many critics, moviegoers and websites were confused whether or not Jenny's last name is Mellor or Millar or Meller. The only thing anyone seems to agree on is that it isn't the common Miller.
Screenwriter Nick Hornby is aware of the accusations of ant-Semitism. He has said the only reason its in the movie is because its historically accurate to the time period and true to the actual events which inspired the film.
A lot of casual anti-Semitism. Additionally, David practices blockbusting, moving black families into apartments to get nearby old ladies out, hence allowing him to buy the apartments cheap.
Also, marriage at 17 being seen as normal and desirable. Not as stark as the other examples, but the idea of girls marrying right out of high school has become a lot less common in the ensuing decades. It is part of the reason that what happened to Jenny doesn't happen as much anymore; today, parents like hers would put a quick stop to any notions an intelligent, academic girl like Jenny had of choosing marriage over going to university. Back then, though, more women did choose early marriage over higher education so it was seen as a viable option, especially to a man like David who is already rich and "established."
The whole notion of teenage sexual activity being grounds for expulsion or refusal of re-admission from school. Nowadays, not only has teenage sexual experimentation become the norm, but even those who are not a fan of it would generally agree that that part of a student's life is not the school's business.