If we are talking about strengths in the sense of Roth's skills as a novelist, these are shown mainly in the mass of realistic detail he gives to support an alternative-history plot some would judge as stretching credibility. All alternative-histories are by definition "unbelievable" because they represent "past" events that didn't occur. But the essence of any kind of fiction is to give untrue occurrences the appearance of truth. In the alternative-history format, writers are even more challenged in establishing verisimilitude, because the public events described in their books are known by everyone to have not taken place.
Roth's strength is that he meets these challenges by using his own factual family (instead of his fictional personas such as Kepesh and Zuckerman) as the center of the plot. The family and their Weequahic neighborhood in Newark are real and described in the specifics typical of Roth's stories. The wider fictional scenario is grounded sufficiently in actual events of the time—Charles Lindbergh's genuinely popularity, the presence of anti-semitism, and the America Firsters who claimed there was a "Jewish conspiracy" to force the US into World War II—that it becomes reality though we know it didn't take place. The prominence of other real-life figures of the time, such as the journalist Walter Winchell, adds to the genuineness in the story. And finally, the outcome in which all of this aberrant history is reversed—Lindbergh disappears and Franklin Roosevelt is reelected, so that actual history is reestablished—is perhaps the novel's most important strength. Though in other hands it could seem an artificially tacked-on ending, Roth works it into his alternative plot in such a way that it's plausible, especially since he associates it with an unexpected but logical explanation of the seeming mystery behind the Lindbergh-as-President phenomenon.
If by strengths in the novel we're talking, on the other hand, about strengths revealed by the characters of The Plot Against America, we would have to point to the author's own family as he depicts them. They somehow remain optimistic in the darkest time when it seems that America is about to follow the path of Nazi Germany. There is a resilience about them and others that allows them to retain their faith that "it can't happen here," though the initial indications have been that it can.