The events of the play all occur during or near an election season. Pacino's character has known the incumbent governor since he was a child as Pacino was a close acquaintance of the governor's father and still has dirt on the family: There are numerous references to a particular evening before the father passed away in which he begged Pacino to burn certain files. The governor, a self-proclaimed man of the people, is looking for "an issue" to tackle as a part of his bid for re-election, or perhaps a bid for the Presidential election, and publicly begins to target Pacino's character for trying to evade paying the $5,000,000 in property taxes on the purchase of the jet, and in the second act has has Pacino officially indicted. Pacino's girlfriend becomes significant because she was on the jet when it touched down, the company claims the cause was a "faulty" low-fuel warning light and not an actual emergency. Due to her connection to Pacino's character, she is physically dragged off the plane and invasively strip searched; this angers Pacino's character as he believes he is "fair game" as a political pawn but his girlfriend should be "off-limits". She is also not a legal U.S. citizen and numerous individuals try to manipulate her status against Pacino to get what they want and his choice to protect her is pivotal in climax of the show.
I honestly don't know if Mamet was explicitly saying or trying to imply that the governor was "in bed" with the airline manufacturer and had them a) change the tail number intentionally and b) make the pilot land so that Pacino would now incur the property taxes that he didn't intend to pay, but that certainly seemed in the realm of possibility. Quite frankly, there are a lot of characters who we hear Pacino talking to on the phone that are not necessarily easy to place in terms of their role in the action, so I could be getting some of the above incorrect; if anyone remembers something differently, please feel free to share!
Ultimately, I thought the issues with Pacino's girlfriend, the governor and the dirt on the family and whether or not he would use it were all very engrossing and I can't say I knew where the plot was going. Perhaps people would think there was more too it if some of these unseen characters were physically present to give the characters and actions more texture.