What are some of the differences between the film and the text of Twelfth Night?
For the purposes of this question I will be refering to the film version of this play that came out in 1996 and was directed by Trevor Nunn, starring Toby Maguire and Helena Bonham Carter. This is an excellent film version of this play and I have used it myself when teaching this text.
The first thing to state is that every single film version or performance of a play is just one "reading" or "vision" of what that play looks like. The job of a director is to take the text on the page and flesh it out; add colour to it and life and turn it into something that is living and breathing. This necessarily involves a number of decisions that make each performance or film version of the play very different from every other.
In the film version, therefore, what is very interesting is that Nunn chooses to create a situation of political tension between Illyria and where Viola and Sebastian come from. There is some danger as Viola and the Captain rush out of the sea and hide themselves, and Orsino's troops look for them. Another key aspect of the play is the way that Viola (disguised as Cesario) is always viewed in very intimate places with Orsino. This adds to the humour, as in one scene Orsino is naked in the bath and Cesario is called to sit next to him. Viola of course is therefore placed in a very difficult position as she is able to see naked the man she loves whilst also having to pretend to be advising him about how to pursue Olivia. Such touches really serve to elucidate the humour in the text and create a memorable film.
Therefore I would take issue with your question. In a sense, there are no "differences" between the text and the film version. Rather, the film version contains one man's interpretation of the text that allows us to see the original genius of Shakespeare more clearly.
If we are using the Trevor Nunn film, then some of the differences are immediate: Shakespeare naturally did not set his play in the nineteenth century, and Viola and Sebastian are not portrayed as a shipboard comedy act in the play. That does not mean that Nunn is incorrect in following the accepted stage tradition of setting Shakespeare's works in other eras; in fact, many of the most successful modern interpretations of his plays use the text to illuminate what is timeless about them.
However, one other significant difference from play to film is that Nunn chose not to elucidate the homoerotic elements in Twelfth Night. The most obvious is Antonio's more-than-friendly feeling for Sebastian, but Shakespeare also "plays" with sexual attraction when Olivia is attracted to Viola as Cesario, clearly a youth that even Orsino (not the most observant of men himself) recognizes as looking just like a girl. Then, at the play's end, there is Orsino's awfully quick acceptance of Cesario as a girl, now not only an acceptable but openly desirable mate.
Since many, if not most, modern Shakespeare scholars accept the idea that Shakespeare himself was bisexual, these elements are some of the more intriguing, and it is interesting that Nunn decided to downplay rather than to emphasize them.