This movie provides examples of the following tropes:
Adaptational Attractiveness: John Keats stood five feet tall in his boots, but that wouldn't work well for the male lead in a romantic movie. For that matter, contemporary accounts describe Brawne more as charming than as classically beautiful.
Brainless Beauty: Brown accuses Brawne of being one. He's wrong, but she's definitely uneducated in comparison to him and Keats. Also, let's face it, she'd have to be quite a Teen Genius herself to have any chance of not seeming brainless in comparison with John Keats.
Brilliant but Lazy: Brown seems to view Keats this way. Yet Keats managed to churn out poems — brilliant poems — at a rate few other poets in history could match. Before he turned twenty-five, he was already too sick to write, but between the ages of twenty-one and twenty-four he had managed to produce literally hundreds of important poems, some of them seminal works of the Romantic Era. Lazy? I think not.
Costume Porn: Personified in one Fanny Brawne, the Coco Chanel of early-nineteenth-century Hampstead. (The film was nominated for an Academy Award for Best Costume Design.)
Dawson Casting: Keats ages from twenty-two at the beginning of the film to twenty-four when we see him depart for Italy; Brawne is eighteen when she meets Keats and twenty-one when he dies. Ben Whishaw and Abbie Cornish, who depicted them, were in their mid-to-late twenties.
...and 24 isn't mid-twenties?
Deadpan Snarker: Brown most of all. But also Brawne and even Keats himself when he's not being all quiet and sullen.
Death Is Dramatic: Averted, which is unusual for Bio Pic. We only find out Keats has died when Fanny gets the news from Brown, and even then we only get a few brief shots of his coffin.
Demoted to Extra: As a result of the film being from Fanny's perspective rather than Keats', Leigh Hunt, Joseph Severn, and everyone else in Keats' life except the Brawne family and Mr. Brown. For that matter, Keats' rivals for Brawne's affection barely even register in the movie.
Foreshadowing: Not surprising, since Keats' poetry and letters are themselves full of allusions to early death.
Forgotten Fallen Friend: Tom Keats, John's brother, who dies of tuberculosis. His death is useful to show that Brawne is beginning to really care about Keats — she stays up all night to sew a beautiful pillowcase for his coffin — but once he's served his plot point he's more or less forgotten by the movie and everyone in it.
Her Heart Will Go On: Not within the movie, which presents Brawne as deeply and inexorably in love with Keats. The Real Life Fanny Brawne married someone else, had children, and lived on another four decades after Keats' death— but only after she had been in mourning for him for six years.
Love Martyr: Brawne — though it's less Keats himself that's the problem and more his circumstance.
Brown's scullery maid is arguably more characteristic of the trope, although she's too minor a character for us to know for sure. (This is true of the Real Life woman, as well— we don't know what became of her.)
Love Triangle: Brawne and Brown nearly come to blows over Keats. Repeatedly.
Man Child: Keats, Brown, and Brawne. Brawne has the excuse that she's barely an adult at all when we first meet her.
And Keats is twenty-two. Brown, however, is in his thirties and has no good excuse for his petulance.
The Muse: Brawne. Although at first she insists she'd rather amuse and be amused than muse, bemuse, or be a muse.
Although the movie generally skips over this, it's also worth noting that Keats had a few muses before Brawne, including a pretty and brilliant young woman named Isabella Jones, with whom Keats shared a "flirtation" that overlapped somewhat with the time he knew Brawne. She has not merely been Demoted to Extra but completely expunged from the movie's account, and in fact scholars don't really know what became of her. (Did Keats dump her for Brawne? Did she dump him to marry someone else with better financial prospects?) For that matter, Keats was perfectly capable of producing a brilliant poem without the involvement of any romantic muse, and only a minority of poems are truly love poems.
Romance on the Set: Ben Whishaw met his now-husband, Australian composer Mark Bradshaw, during filming.
Rule of Drama: It's a Bio Pic, not a documentary, so the lives of Keats, Brown, and Brawne are streamlined from the messiness of real life into a borderline-melodramatic romance. Anything that doesn't further the plot is pushed to the side or completely cut. Conversely, things that never happened are added, for the same reasons.
Separated by the Wall: In separate but adjoining bedrooms, Keats and Brawne each lie abed and place a hand on the wall, to make it seem as if somehow, by magic, their hands are touching. Neither of them has any way of knowing that the other is doing this at all, yet their hands still align perfectly.
Tear Jerker: The movie doesn't skimp on them, but most of all the scene in which Brawne learns that Keats has died in Italy. Arguably, also the scene in which Brown admits he's failed Keats, his one true friend.
Teen Genius: Not literally a teenager, but Keats is only twenty-two at the start of the film.
Theme Naming: The Brawne sisters: Fanny and Toots. To some extent, an example of Having a Gay Old Time, as they were common nicknames in that era. Be that as it may, if Shakespeare had had sisters named Fanny and Toots alongside Mistress Quickly, you can bet that the local countryside would have teemed with such Country Matters.
Tragic Dream: Brown dreams of being a great poet, like his friend Keats. Keats dreams not only of being great poet — not realizing her already is one — but also a critically and financially successful one. (Financial and especially critical success would come in time; alas, not before his death.) In addition, Keats dreams of marrying Brawne, but he has no money and few prospects.