How does Lee develop Tom Robinson's three-dimensionality and make him a key character? How is Tom Robinson a well-rounded character?
Tom is the quintessential mocking bird. He is well-developed because the so much of the story is about him--directly and indirectly.
We learn about Tom as he speaks, through his actions, by where he lives and how he dresses, and by what others say about him. The scenes in the courtroom are especially helpful in developing his character as we get the story from three different people: Tom himself, Mr. Ewell, and Mayella Ewell.
We learn about Tom from many characters in the book. Calpurnia, Atticus, members of the black church, the Finch's neighbors, and others in the book discuss Tom and his situation. From all points of view, we come to know Tom as if he were our own neighbor.
We know his physical description--he is a beautiful man. He works hard, is kind, has nice teeth and a loving smile. He helps out the less fortunate than himself and expects no payment for it.
The only flaw in Tom's appearance is his disabled left arm due to an accident with farm machinery when he was young.
There are no flaws in his character. He was just in the wrong place at the wrong time.