Unrequited Love
As depicted in classic playwriting such as Shakespeare's, people have longed to be in love because love makes us happy and fulfilled. That is, unless it is a love that is unrequited. Being in love with someone who does not reciprocate your feelings is utterly miserable, and this is one of the key themes of the film.
Although the film ultimately offers a series of happy endings, the characters suffer immeasurably for their love. Orsino is in love with Olivia (who is disdainful of him at best, and otherwise completely disinterested.) Olivia is smitten with Cesario (Viola in disguise) and wants nothing more than to marry "him". Malvolio also wants to be married to Olivia but by the end of the film has come to terms with the fact that she is basically out of his league, and feels rather silly about the whole thing. The main "love triangle" in the film is in fact comprised entirely of people who are in love with another who does not feel the same way about them.
Twelfth Night
Twelfth Night was a time that was celebrated in England since Pagan times, and in Shakespeare's day, it was also a time when there was a strange willingness for social hierarchy to be turned upside down. Whereas the class system in England would normally preclude the movement between classes by way of marriage, on Twelfth Night what was usually unacceptable became acceptable. This is how Maria managed to elevate her status by marrying Sir Toby Belch, and it is also somewhat mitigating circumstance in Malvolio's idiotic pursuit of Olivia, a noblewoman who would never dream of marrying anyone who was of a lower social class. If there was ever a time for him to pursue this seemingly unattainable ambition, Twelfth Night was definitely the time.
Gender Fluidity
Most of the confusion, heartache and even comedy arise from the fact that the main character, Viola, is a female dressed as and assuming the identity of a man. This is sometimes called a "trouser role" and also less kindly called a "transvestite comedy". Viola is in love with Orsino but cannot tell him because she is supposed to be a man. However, even when he realizes that she is a girl he is still attracted to the notion of her as a woman who is cross-dressing. There is also an ambiguity in the relationship between Antonio and Sebastian who are close friends and rarely apart; although Sebastian marries Olivia is is implied that it is more for her status, money and beauty than for his general attraction to her as a woman. Throughout the movie there is a gender ambiguity and fluidity that is sometimes spoken but often not, left up to the audience to read for themselves
Class Divide
There is a glaring class divide in Shakespearian England and this is thematic throughout the movie. It is most clearly illustrated by Malvolio's crush on Olivia which is exploited for amusement by Sir Toby and Andrew Aguecheek. As a noblewoman Olivia would never consider a relationship with anyone of a lower social class - it would also lower her own status - and he should be aware of this. HIs determination to cross the divide is what makes his friends find him so ridiculous and foolish. The nobility also take many staff members, servants and pages into their households and the structure of the house is also shown within this theme.