While the story is a very close look at a family, Agee uses the omniscient third person to separate the characters and reveal their inner conflicts as well as their own viewpoints of their interactions.
As mentioned, I suspected some underlying tension between Jay and Mary as Agee displayed their hour together just before Jay leaves to visit his dying father. Once Agee has them separated, we are privy to their reflections. While Jay drives toward home, we see not by specific references to Mary that there is a problem, but rather by the joy he takes in being alone and driving away from her and his home. Agee then takes us back to Mary, unable to go back to sleep after Jay’s leaving, and her turmoil over her feelings towards his father, his family, and Jay himself. Mary evidently has a very strong grounding in her religious beliefs, and a good portion of her conversation is in asking God for forgiveness for her uncharitable feelings. A morning scene with her children where Rufus insists on answers about God reinforces what Mary herself has let us see.
Prior to Jay’s arrival at his family home, we are once again given a glimpse of the family dynamics, and it is obvious that his brother, Ralph, is an alcoholic desperately wanting to be the son his mother and father expect, and yet feeling himself substandard, seeks solace in booze.
There is a definite focus on the strengths and weaknesses of each of the main characters, the plot being carried by their interaction and in how they each stand up to the problems that come up.
There may be some overwriting here, some overemphasis on certain points that tend to get the least bit tedious, but overall, the tension is maintained throughout.