The lead characters are played by John Hurt, who turns in an excellent performance as Arthur Seldom, and Elijah Wood, who turns in an eponymous performance as the student Martin. The supporting cast is likewise varied: in the luvvies-we-like category I place Anna Massey and Jim Carter; in the wooden category we also have Burn Gorman.
The film is broadly faithful to the book, and some of its enhancements (such as the replica Enigma machine in Mrs Eagleton's house at the beginning, or Seldom shouting at a group of workmen digging up the road) fit rather well. The brick-sized mobile phones are appropriate to the time (1993), even though it seems unlikely that even an American graduate student would possess one. On the other hand, the film does show its foreign heritage: the scene between Martin, Seldom and Lorna seems too Latin to me, and the blunder about the police routinely being armed in the UK is carried over from the book. The concert music was disturbingly cacophonic in the same way as a concert rehearsal we'd heard while going round the city museum at St Mark's in Venice - I rather suspect a more traditional piece would be the typical fare for a fireworks gala concert at Blenheim. This was redeemed by closing the film with the theme from A Musical Offering, an appropriately Hofstadterian polymathic conclusion. I'm not sure why the film-makers chose to rename Fermat to Bormat and change Andrew Wiles' name - no doubt there were reasons, but that again is a broadly chronologically accurate detail in the book, and it did sadly put too many images of Sacha Baron Cohen into my mind. Number theory - iz nice?
I can confirm that the space-time wormholes we are all familiar with from Morse are fully functional. In particular, The White Horse seems to have leapt from one side of Broad Street to the other.
There is not so much a simplification of the plot, but a certain pedagogic exposition of it, in an attempt perhaps to make some of the more rarified themes more accessible. Judging by the audience size in a cinema outside Oxford, though, I'm not convinced it was worth that particular effort.
In summary, if you enjoyed the book, I think you will probably enjoy the film.