What "generally accepted truths" does Atticus challenge in is final appeal in To Kill a Mockingbird?

I believe that you are talking about Atticus's speech in Chapter 20.  In that speech, he challenges a few generally accepted truths.  The first of these truths is that black people lie all the time.  The second is that any incident between a white woman and a black man is the fault of the black man.  (This second assumption was behind many of the lynchings of black people that actually happened in the South in our history.)

Atticus says that the testimony against Robinson was based on the idea that no one would believe Tom because everyone knows that "Negroes" lie.  He also says it is based on the idea that black men are constantly lusting after white women and cannot be trusted around them.  Atticus argues that neither of these is true in this case.