Daniel H. answered 10/29/19
Over fifteen years in Film & Video, Specializing in Post-Production
The Director or Producer would make that decision as the film is being shot, most of the time. He or she would then relay the message to the Script Supervisor, who would write down the Rolls, Scenes, Takes and Timecodes of said bloopers. This would later be given to the Editor via EDL who is responsible for Logging, Capturing and/or Transferring footage, as additional material to import. The Editor in charge of Assembly would work closely with the Titles & Opticals specialist to make sure the credits are formatted in such a way to accommodate the blooper takes.
Conversely, if it's a lower-budget film and the Director, Producer, or even Writer wishes to be in the editing room with the Editor in charge of Assembly, the decision can be made right then and there. The nice part about this is this footage generally does not need post-processing through color correction, VFX, surround mixing, etc., mainly just syncronization with the boom and that's it.