The treatment of Von Braun in episode 2 was repulsive. No one knows the full story of his knowledge of slave labor used in V2 production. The show used all of the accusations against him but failed to also mention that Von Braun was once arrested by the Gestapo under suspision of disloyalty. Hardly something they would do if he were a trusted nazi as portrayed in the show. They could have covered both aspects but chose to only cover the negative.

Apollo 24 is needed to go to the moon to rescue an astronaut stranded there for months. The entire Apollo 24 rescue launch was a daisy chain of errors. The booster flight computer fails so they can't make a TLI burn. So another flight brings up a new computer and they EVA over and install it. They make all the connections with half of both crews still on EVA and of course it fires up unexpectedly and one Apollo 24 crew member is killed by the engine plume and the rescue Apollo CSM is dragged along with it for a while being towed by an astronauts EVA umbilical (which would have snapped instantly but, this is Hollywood). A24 burns the entire fuel load and goes off roughly in the direction of the moon (what luck!) but will miss it by a thousand miles or so. Meanwhile a crew member of the other flight is floating free in space but they recover her without too much drama (but plenty, of course) and return to Earth.

A24 burns all of its service module fuel to get almost close enough for lunar capture, but not quite. If they (the remaining 2 crew includes Deke Slayton and a female, lesbian, commander) miss they go off into deep space forever. (In reality they would not have, not enough velocity but this is Hollywood). So the guy stranded on the lunar surface launches (after a scrounging for more fuel drama of his own, with help from a cosmonaut) into orbit with extra fuel for the A24 CSM, which he can't dock with because it's tumbling and it's going to go blasting past anyway and not enter orbit (which means he could not have rendezvous anyway without matching velocity and being on a course into deep space himself, but again "Hollywood").

So they can't dock. Lunar astronaut with rescue fuel just shoves a container of about 100 gallons of fuel toward the stranded CSM from about 100 yards away. Could have gotten closer than that with no danger but doing so would not have generated the required level of drama and he would not have missed, as he did, and then the female commander of the A24 CSM would not have to launch herself out to catch and retrieve the fuel, as she did. She celebrates and tells Deke she has the fuel but Deke has died of injuries sustained when this all started going south in the beginning. (not the only real world person they've killed in the series, they killed Gene Kranz who is actually still alive as of this comment so I wonder how he feels about it)

And now the last remaining member of the rescue crew and the stranded lunar astronaut are back on the moon. Tada! No explanation of how they got the fuel into the CSM or how 100 gallons of fuel was capable of braking a 30+ ton spacecraft into lunar orbit. And then shortly thereafter the original astronaut who had been stranded on the moon returns to earth on that same CSM with it's 100 gallons of fuel or I suppose even more fuel that was brought up to it from the moon from other sources they scrounged up, despite they just barely being able to find the original 100 gallons or so, but did not explain.