I would suggest to Jem that he must try not let his emotions build up inside him. Perhaps pointing out the change in his personality was caused by his disappointment in the experiences around him and that instead of becoming distant and cynical he talk to those who love him. I would also tell him not to shut Scout out just because of her age. She could be instrumental in helping him sift through his conflicting emotions.
I would tell Jem not to give up on people. He's witnessed some brutal things at his age--the unfairness of Tom's trial, the vengeance of Bob Ewell, the hypocrisy of adults he's trusted. These all happened in those awkward years between being a kids and trying to become a teenager and an adult. Jem may get a sour view of adults and turn into another Holden Caulfield. However, Jem should look at the good around him; people like Link Deas, Miss Maudie and especially his father. I would tell Jem to always trust and listen to his father, and to look out for his little sister. Also, think for yourself. Don't let yourself get caught up in what everyone else is thinking. Do what you think is right, but think before you do it.