The middle school scenes were shot at the now-defunct Patrick Henry High School in Stockbridge, Georgia. This is the same location used for both Hawkins Middle and Hawkins High Schools in seasons 1 and 2 of Stranger Things (2016).
Brandon Breyer's name follows the classic comic-book convention of superheroes with alliterative first and last names, such as Clark Kent, Peter Parker, Bruce Banner, etc.
Brightburn is mentioned as being in Kansas - and Brandon's dad's truck license plate is Kansas-issue - which is where Kal-El landed and later grew up to become Superman.
In many scenes, Brandon wears combinations of blue, red and yellow, the main colors in Superman's traditional outfit; This motif was also used on the character Clark Kent in the TV series Smallville (2001).
At 31:52 when Brandon's mother is typing in "Kansas" into the Google search bar, the list of suggested matches include "Kansas meteorite" & "Kansas Metropolis" which is a crafty reference to the Superman/Clark Kent character who grew up in Kansas and worked in Metropolis.