The examples you have a good. Reading to Mrs. Dubose should Jem that his actions have a reaction and there is usually more to people that we generally see. The trial obviously opens Jem's eyes to the injustice in the world, and allows him to think critically about the world around him (look at the discussion he has with Atticus about the legal system). The incident with Atticus shooting the rabid dog, Tim Johnson, shows Jem the a gentleman does what needs to be done when it needs to be done.
There are several other examples of Jem growing up. When Nathan Radley cements up the knot hole that Boo had been leaving gifts in, Jem begins to cry. He obviously knows that it was Boo's only way to communicate and Nathan is preventing that. Also, Jem tells Atticus that Dill has run away and Scout explains that by doing this, Jem "broke the final code of childhood." Jem stands up to Atticus when the mob tries to attack Atticus to get at Tom Robinson--a very grown-up thing for Jem to do. Another small example is when Scout and Jem are sleeping out on the porch, and Scout is about to squish the roly-poly bug. Jem tells her not to do it, as it didn't do anything to her. Jem has learned the adult lesson of empathy.