Irony of Big Brains
The human race considers themselves superior to other species because of their big brains. However, according to Leon Trout, these prized big brains led to the downfall of the human race.
Irony of Deathbed Wishes
Most final deathbed wishes are made to help one's relatives. Roy Hepburn probably thought he was helping his wife by making her get over his death. To most onlookers who know that the ship was going to be shipwrecked, this was, ironically hurting Mary more than helping her. But they too are wrong, ultimately, getting shipwrecked on the Galapagos saves Mary from the financial disaster and disease. Roy Hepburn sure has foresight.
Irony of Leon Trout's Hope in the Human Race
After experiencing many horrific events in Vietnam and going AWOL, one might think Leon Trout has lost hope in humanity and wants to live his life out in peace away from the failed species. Ironically, Leon Trout chooses to stay 1 million years observing the species that has so many problems and has caused him so much pain.
The Irony of the Pinnacle of Human Invention: the Mandarax
At the time, the Mandarax was the most advanced computer invention, invented by the best and the brightest of the human race. Ironically, when finally put to use, the Mandarax just simply spews out useless quotes that only confuse the user more.
Irony of James Wait
James Wait is born into scamming and swindling, and he continues to do it throughout his adult life. One might think in the last moments of his life, he will stop lying and swindling. Ironically, he doesn't and he remains a consistent character throughout the book by marrying Mary Hepburn (and stealing her inheritance) in the last moments of his life.