Though readers follow Scout, the narrator in To Kill A Mockingbird, as she matures and begins to understand the important lessons her father teaches her, Jem is the character who matures the most over the course of the novel. 

Part 1 of To Kill A Mockingbird focuses mainly on the children's obsession with Boo Radley.  Though Jem is older than Scout and Dill, he encourages, and even organizes, attempts to lure Boo out of his house or communicate with him in some way or another.  Atticus continually reminds the children to leave Boo alone, but the mystery of the Radley house is too tempting for them to forget.  As the eldest of the children, Jem should be the one to heed Atticus's orders to leave Boo alone, so his failure to do so might be seen as a weakness.  However, readers must remember that though Jem is older than Scout and Dill, he is still a child. 

I think the best example of Jem's weakness--if we can call it that--is the impulsivity he displays at the end of Part 1.  After Mrs. Dubose insults Atticus, Jem chops down all of her flowers in a fit of rage.  Again, though Atticus consistently teaches his children not to retaliate when people speak badly of him, we must remember that Jem is only a child and that children are often impulsive.  Also, Jem learns a valuable lesson in courage by spending time with Mrs. Dubose as part of his punishment. 

Part 2 of the novel marks a period of immense growth for Jem.  In Chapters 12-14, readers watch Jem mature; Scout notes that Jem is moody, inconsistent, and acts as if he is superior to her and Dill--behaviors that annoy Scout very much.  Also during this time, however, Jem begins to exhibit a better understanding of the world around him.  As the focus of the novel shifts to the trial of Tom Robinson, Jem sees--and is disgusted by--the injustice that exists in the town of Maycomb.  In the incident outside the jail in Chapter 15, Jem openly defies Atticus when Atticus orders him to leave--a decision which shows that Jem understands the danger of the situation and knows that it will only escalate if he takes Scout and Dill home. It takes courage for Jem to defy his father, but he does so because he is developing a mind and will of his own, along with the maturity to make responsible decisions.  Thus, Jem's moral development, compassion, and  sensitivity in Part 2 can be seen as his greatest strengths.

For a physical description of Jem, see Chapter 15; Scout, while watching Jem defy Atticus, observes that while Jem possesses his mother's physical features (she describes them), "mutual defiance" makes Jem and Atticus seem to look alike.

Jem's weaknesses are mostly evident at the beginning of the novel, when he is still a child. He makes fun of others including Scout and Dill, and initiates rather hurtful, childish games based on his own imaginings of Boo Radley's life. He's embarassed of Atticus as well, feeling that he's too old to do anything useful. He also has difficulty controlling his anger. Although he's better at it than Scout, on at least one occasion he loses his head, attacking Mrs. Dubose's bushes with Scout's baton. Finally, although one wouldn't want to fault a child for this, Jem seems to be overly hopeful/optomistic- too willing to believe that everything will turn out right in the end. For example, he really struggles with the verdict in Tom's trial, because he knows it's so clearly wrong.

As for his strengths, he has many. He's physically strong, and enjoys playing football. He gradually grows into a beacon of morality in the novel, knowing that the racism and discrimination of Maycomb is inherently wrong. He learns a great lesson at Mrs. Dubose's bedside, although he hates every minute of his punishment. Still, he learns about courage in the face of insurmountable odds. This helps him gain respect for Atticus, as he does throughout the novel. Finally, Jem is compassionate, and cares for others- especially Scout. When Scout is attacked by Bob Ewell, Jem rushes to her defense without regard for his own safety.

There isn't much in the way of a physical description of Jem. For information on his clothing, you'd have to search particular scenes (for example, when he loses his pants on the Radley fence). The first paragraph of the book offers a bit more:

His left arm was somewhat shorter than his right; when he stood or walked, the back of his hand was at right angles to his body, his thumb parallel to his thigh. He couldn't have cared less, so long as he could pass and punt.

However, this is after the majority of the novel takes place, so this isn't how Jem looks throughout most of it. Again, there are some physical descriptions, mostly about his hair and eyes, but these are all scene specific- although we do learn that both are dark.