There is no doubt that the prominent theme of The Appeal is both corporate and government corruption.
In regard to corporate corruption, the chemical company in the novel is happily spewing pollutants that cause cancer in both humans and animals. The chemical company simply doesn't care, is only interested in making money, and is happy to hire big-wig lawyers to do their dirty work in the court system. The company even goes so far as to investigate and accuse the two lawyers of the opposing side (Mary Grace Payton and West Payton). The company desperately wants to win the appeal.
In regard to government corruption, the focus is upon the court system and on Congress. Greed is a main focus here, as evidenced by the following quote:
In Washington, money arrives through a myriad of strange and nebulous conduits. Often those taking it have only a vague idea of where it's coming from; often they have no clue. In most democracies, the transference of so much cash would be considered outright corruption, but in Washington the corruption has been legalized.
There is a senator who knows companies who rig elections. It is this senator who focuses his attention on the elections for the Mississippi Supreme Court in order for the chemical company (see above) to win their case. Further, there are candidates randomly inserted into the campaign in order to take the focus off the one honorable judge.
Amid nasty and brutal elections and courtroom drama, we learn all about corruption from both the corporate and the governmental point of view.