The seasons
As the film opens on a clear blue LA sky, we hear various radio stations playing from different cars. The first we hear announces the weather: "another hot sunny day today here in sunny California. Temperatures 84 for downtown Los Angeles." It is ironic that, even though the film itself is structured around the seasons—which metaphorically acknowledges time passing and change within that time—it should open with the clear message that the seasons in fact change very little in LA. As though the bustle, the weather, the mood of L.A. will keep on going, even as the weather metaphorically changes for Sebastian and Mia.
The title: La La Land
It is ironic in a film that sets up the the creative ambition to make it big as a fantasy (that which people go to "la la land" to pursue) that it is in fact the interpersonal romance, and not the Hollywood dream, that does not survive. In this film, you are living more in la la land by believing a relationship can last than you are believing in realizing your dreams.
Sebastian's dream
Mia is angry with Sebastian for spending time on the road with his band, when he is supposed to be starting his own club. The argument about this comes at a time when Mia is seeing less and less of Sebastian and her frustration must have a lot to do with that. The irony, of course, is that when Sebastian finally chooses to dedicate himself to opening his club, it is this that stops him from following Mia to Paris and ends their relationship.
Acting
Mia wants to be an actress, and we see her playing different parts throughout the film. None of these opportunities, none of her acting efforts start her on the road she wants to be on. The irony of course is that when she plays herself in the final audition of the film, when she tells the story about her aunt, she is finally given the opportunity to launch her acting career, to start playing other people.