What finally forces Jem over the treshold toward adulthood? What symbolic incident occurs that testifies to Jems move toward adulthood?
This question is really good. Harper Lee's novel To Kill a Mockingbird is certainly a novel of development (or a Bildungsroman, to use the fancy term), but most discussions seem to focus on Scout. Jem's development seems to be less frequently discussed, although he's the one in the Finch family who's experiencing the most changes.
For me, the single most important scene that signals Jem's movement toward adulthood is his refusal to do what his father says when Atticus tells him (and Dill and Scout, who are with him) to return home and to leave Atticus alone to deal with the mob of Old Sarum men outside of the jailhouse where Tom Robinson is being kept the night before the trial. Anyone reading the novel today can be pretty sure that the mob of men smelling of "stale whiskey and pig pen" have come to lynch the black man accused of raping a white woman. However, at least one of the children in this scene (Scout) has no clear sense of the danger faced by her, her friend, and her family at this moment. Jem seems to have a much fuller awareness of what is occuring and, in refusing to yield to his father (in what would be an act of blind obediance), he shows a new maturity in his behavior. His refusal comes not out of infantile rebellion but rather out of an awareness of what is happening and what needs to be done. Jem, not Scout -- I believe -- is the one who shows bravery at this point in the story.
There are no doubt other possible answers to this question, of course, and I look forward to hearing some!