I think that this becomes one of the most significant elements in the drama.  To a great extent, the problem of appearances and reality hits everyone in the drama.  On one hand, Maggie finds herself immersed in the fundamental challenge of conforming to a standard into which it is impossible to fit.  She should be bearing children and should be the happy mother with a family to her name.  Yet, her husband is unable to provide this for her and she must accept the burden of this social stigma, something that children already understand in the drama.  Her ending line to Brick about the need to "make the lie true" represents how tormented she is, knowingly or unknowingly, about the dynamic between appearances and reality.

Big Daddy is driven to live a life outside of "mendacity" or the idea of lying. His relationships, though, are predicated upon deception or denial of him having cancer.  When he comes to know this deception, it brings to light questioning of everyone and everything around him, including a marriage of over four decades.  In the end, Big Daddy is no closer to understanding the reality of the world, in terms of what constitutes lies and what constitutes reality.  This becomes one of the elements that define his character and something that drives him throughout the drama.

Brick also struggles with the dynamic of what is truth and what is false.  Brick struggles with what his feelings towards Skipper actually are and how emotionally uninvested he is in a world that dictates his need to be involved.  It is here where I think that Brick struggles with appearances and reality.  In this construction, one sees how Brick wishes for reality, but also understands the pain that accompanies it.  For this reason, Williams constructs his character as one that possesses "emotional paralysis," a condition that prevents him from taking action.  In this, Brick becomes paralyzed by the fluid dynamic of appearances and reality, something that impacts the main characters in the Williams' drama.