Critical Research Failure: On the part of the Rivington men, who failed to anticipate how popular their rations would be among the Confederates. Even more than a lack of arms, the inability to keep the army properly supplied played a huge role in the defeat of the South, something that has been well documented by historians.
Fridge Logic: Isn't it peculiar that nobody - not even General Lee, when Andries Rhoodie told him that he and his compatriots hailed from South Africa - made the connection with the Boers/Afrikaners? In the mid-1860's, two of the best-known events in Afrikaner history, the Battle of Blood River and the Great Trek, were already several decades in the past, and a well-educated, savvy person like General Lee ought to have been able to figure out from where they came. (Of course, it does turn his thought "Dutchmen they are" when he hears the accents of Rhoodie's friends into an example of Hilarious in Hindsight.)
Funny Moments: A Confederate chemist at the Tredegar Ironworks figures out that the active ingredient in some of the Rivington Men's future explosives is nitroglycerine... which is also the active ingredient in the heart disease treatment tablets they've been giving to Lee. Lee is briefly convinced they're attempting to assassinate him by feeding him explosives.
Genius Bonus: Several lines of dialog spoken by the historical characters are things they actually said or wrote, just in different context; only a historian or Civil War scholar could get them all. As one example, Robert E. Lee says "Let the tents be struck" after the war ends in both reality and Turtledove's novel, the only difference being that in the former he lost and in the latter he won.
A variant of his last words, which were actually, "Strike the tent".
Another one from Lee when discussing future military advances with Rhoodie: "It is well that war is so terrible, or we should get too fond of it."
In one scene, Lee calls for his aide by saying "Mr. Marshall, come quickly, I need you"; this is (supposedly) the first phrase ever transmitted via telephone (except of course for the proper name; Alexander Graham Bell's assistant was named Watson).
Moment of Awesome: When Robert E. Lee (having acquired an up-time textbook) realises that the Rivington Men do not represent the mainstream of views on race in the future, and he delivers what to Rhoodie must be the ultimate insult: "You and your men are as out of place in your time as John Brown was in mine."
The Confederates defeat a machine-gun by tunnelling under it and blowing it up (the Battle of the Crater in reverse, thanks to the presence of an ex-Union officer who was a key instigator of the scheme in the original timeline).
Moral Event Horizon: The AWB crosses this in the eyes of the Confederacy when they attack Lee's inauguration with Uzis in an attempt to kill him, spraying bullets all over the place and killing countless civilians, including Lee's wife Mary.
This is also a case of Reality Is Unrealistic, because the Confederates are outraged that anyone would try to assassinate a president in such a way and sure that none of their own people would do such a thing, not knowing that in the original timeline John Wilkes Booth would have done just that to Lincoln. (Although Booth acted without the sanction of the Confederate government and there were no innocents killed there. To be fair that would be hard using a single-shot pistol like Booth did.)
And that's the point: assassinating a president is bad enough, but it's the deliberate killing of large numbers of innocent civilians in the process that sends the attack clear over into Moral Event Horizon territory.
In fact, Lee already did know from the Picture History of the Civil War that Lincoln had been assassinated, and this very thought flies through his mind during the Richmond Massacre.