"For All Mankind" episode one concluded with a pretty terrifying cliffhanger: Imagine crashing your spaceship on the moon with no clear solution on how to escape. However, "He Built the Saturn V" quickly gets Neil Armstrong and Buzz Aldrin off the lunar surface and back home safely. (It wasn't necessarily the smoothest journey, but as was mentioned in the previous episode, "any landing you walk away from.") And then, it's all about NASA bouncing back from the ego blow of losing the race to the moon, somewhat fortified by the success of Apollo 11.

What President Nixon wants — and what the military does too — is for NASA to focus on "the race for the base," specifically the creation of the first permanent military installation on Mars. Werner von Braun is strongly against this idea, after his past experience where his work was taken away from him and given military application.
Ed is still trying to figure out what to do with his current position in Siberia — returning to the Navy is an option, except that his wife hates it, as she prefers the space program to constantly worrying about his plane getting shot down. A potential path to personal redemption comes when Congressman Charles Sandman, with the support of Nixon, asks Ed to testify in front of the committee investigating NASA's failures. Ed is basically asked to say what he already said in the pages of Newsweek, and is told that if he does so, he'll be back in the space program. But instead, he tells the committee that he was the commander of the Apollo 10 mission, and the ultimate decision to turn back instead of pushing their limits and going to the surface was his. He also resigns from NASA, resigned to going back to the Navy.
Ed's testimony makes no one happy, but the committee (and Nixon) has other ways to get around von Braun's unwillingness to support the military moon base. The solution ends up being to tell the truth, or at least one part of it. Von Braun's committee testimony ends on an ugly note when Rep. Sandman confronts him with the brutal truth of his time working as a scientist for the Nazis, specifically that his V-2 rockets were built by prisoners at Mittelbau-Dora concentration camp, and much death resulted. (All of this is right there on von Braun's Wikipedia page for clarity.)
The resulting ambush is heartbreaking to watch, because up until now, especially as seen through Margo's eyes, von Braun has always been a kindly figure. But he did know, and thus he is clearly on the outs thanks to his poor public performance. Hearing him say "progress is never free" breaks Margo's heart (and he had just given her his special slide rule!), but it ends up being good news for Ed because Deke asks him to come back to the program after all — specifically to be a part of Apollo 15 again.
Regarding the "race to the base," at this juncture, it remains uncertain, even if Nixon publicly declares that they will do "whatever it takes" to propel America's journey into space. As the episode unfolds, an unsettling question may cross your mind: Are we... rooting for Nixon? After all, we want to support the space program, don't we? And Nixon is bolstering the space program with even more resources, but it's Nixon, for Pete's sake. Perhaps this new alternate reality will lead to a kinder, gentler Nixon? That seems highly unlikely.
A significant detail is casually dropped near the end of the episode: During a news broadcast preceding the launch of Apollo 12, Nixon announces that Henry Kissinger is now engaged in negotiations to end the Vietnam War. Given that, in our timeline, the war wouldn't conclude until 1975 (after numerous fatalities), this says a lot about the country's new priorities and is also one of those choices with potentially immeasurable repercussions. (Just consider how many Vietnam War movies may never get made.)
"He Built the Saturn V" is primarily a place-setting episode that may be crucial for future storylines but lacks its own momentum. However, it does conclude with another bombshell: Apollo 12 launches almost simultaneously with another Russian expedition. And this one brings a new surprise for the Americans - the new cosmonaut on the moon's surface is a lady. So the Russians can now claim both the first man and the first woman on the moon. Your move, America.