Corrected entry: During the opening credits a map of Great Britain is shown (to help those who don't know where London is). Many of the rivers on this map are completely wrong. For example the Medway doesn't start south of London, and there is a river flowing North through the Surrey/Hampshire area which, given the hills there, isn't possible. (00:01:30)
Corrected entry: When Emma sits in her bedroom looking out of the window at night, her hair hangs loose and is thick and long. It seems only in that scene Gwyneth Paltrow wears a wig. If all that hair were to be piled on top of her head as it is in the rest of the film, the hairdo would be a lot more voluminous than what we see.
Correction: I don't see this as a mistake, and am not at all convinced it's a wig. It's much easier than you'd think to get thick hair into a tight 'do when you put it up.
Correction: The map shown during the opening credits is a drawing made by Emma herself, so she drew London and the town they're living in.