The Danish title 'Hævnen' translates into English as 'Revenge'. Susanne Bier mentioned that she prefers the English title 'In a Better World' which emphasizes the hopefulness of the film while the Danish title emphasizes the severeness of the film (at 1:52:49 in the Blu-ray director's commentary).
At 13:37 in the Blu-ray director's commentary, Susanne Bier notes that Elias' braces were Markus Rygaard's own braces, not filming props. Having the bullies call him "rat face" was devised after casting, reasoning that, were he bullied, it would be in part for the braces.
Susanne Bier mentioned that the meeting of Elias' mother with Christian's father in the headmistress' office was originally longer and was the first scene of a story line in the script that brought Christian to the belief there was a budding romance between them. Most of that story line was cut during editing because there were too many story lines (26:19 in the Blu-ray director's commentary).
The story that Christian reads at his mother's funeral is Hans Christian Andersen's "The Nightingale".
It took just three weeks in Danish cinemas for the film to turn a profit, according to the studio Zentropa.