Two examples of Jem's innocence are in chapter 5 and chapter 21 of To Kill a Mockingbird.
In chapter 5 Dill and Jem devise a plan to communicate with Boo Radley by attaching a note to the line of a fishing pole and placing the note on a window sill. While Jem is attempting this act, Dill holds a bell that he will ring if anyone is coming towards them. Soon thereafter, Scout hears Dill frantically ringing the bell in Atticus's face. Having headed home for a file he had forgotten to take with him that morning, Atticus has caught Jem in the act of trying to send a note to Boo. When he scolds the children to leave the Radleys alone and not to play "an asinine game" or ridicule anyone in the street through play-acting, Jem interrupts,
We weren't makin' fun of him, we weren't laughin' at him . . . we were just—"
"So that was what you were doing, wasn't it?"
"Makin' fun of him?"
"No," said Atticus, "putting his life's history on display for the edification of the neighborhood."
Jem seemed to swell a little. "I didn't say we were doin' that, I didn't say it!"
Atticus grinned dryly. "You just told me," he said. (Ch.5)
In his innocence, Jem is tricked into revealing what he has been doing. As he tries to prove his lack of guilt for the charges, he defends himself by listing what he and Dill have not done, omitting only the charge which Atticus surmises. Angry at Atticus's cleverness, he shouts after his father who walks back to his office, but is out of hearing range, "I thought I wanted to be a lawyer but I ain't so sure now!"
In chapter 21 Jem suffers the loss of his belief in justice. In his innocence, Jem believes in absolutes. If the law is written and the courts have proper procedures followed and positive proof is given regarding the guilt or innocence of the defendant, then a jury of twelve men should act with integrity and vote for the verdict that is just. So, even though he has been previously alerted to the hatred among some of the townspeople and the visceral feelings of the lynch mob, Jem is idealistic and innocent enough that he believes the jury to be rational men who will base their verdict solely on the evidence.
At the courthouse, while the jury is out deliberating the verdict, a smiling and confident Jem remarks to Pastor Sykes: " . . . don't fret, we've won it. . . . Don't see how any jury could convict on what we heard." (Ch.21) However, the wise and experienced Reverend Sykes, who himself suffers injustice under Jim Crow, cautions Jem to not be so confident: "I ain't ever seen any jury decide in favor of a colored man over a white man . . . " (Ch. 21)
Sadly, Reverend Sykes proves to be right. Jem is brought to tears over the injustice of the verdict, his faith in the legal system shattered and his innocence lost. No longer can he have faith that members of a jury, who swear to do their legal duty, will be forthright.