The narrator says that after the initial nuclear apocalypse, "It took two million years for the clouds to disperse." This would be more than enough time for the nuclear material to decay to harmless levels, which invalidates the premise that dangerous radiation still lingers in the world.
After receiving the news about the assassinations of the heads of his neighboring states, Blackwolf declares that the successors will blame the deaths on people in their own ranks. But Blackwolf is the only ruler who still uses technology, and his assassins are armed with automatic rifles. Blackwolf will immediately be blamed.
When Avatar is telling the president about his brother, the narrator says that Blackwolf has been studying black magic for 5,000 years. But when Blackwolf is introduced, it says that the story takes place 3,000 years later.
Just before Avatar's party sets off toward Scortch, the narrator tells us that Elinore visits her village to "say goodbye to her father," etc. But her father--the president--is already dead (to wit, murdered by the robot assassin), as Elinore herself tells us moments later. Actually, this is not a goof. In the illustration accompanying this narration, Elinore is shown kneeling in front of her father's tomb in prayer. This is what was meant by "saying goodbye to her father."