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).
(at around 1h 27 mins) One of the medical staff mentions Elias is 12 years old. At around 13 mins, their teacher notes that Christian and Elias have the same birthday, so Christian is also 12 (the same age that William Jøhnk Nielsen was during "filming").