Ah, of course they had to do an episode about the Apollo 11 moon landing.
But that's fine, space flight is always cool.
A bit of a mixed bag. I liked that they included Katherine Johnson as a part of the story. I also liked that Flynn's plan to mess with the moon landing was based on a real problem they had, so it made sense to exploit that (although he also could have screwed with the mission at a much earlier time that wouldn't have involved a computer problem for Rufus to fix). Both of these elements are interesting pieces of history that I can't say I've seen used in historical fiction before.
Their depiction of technology was a dud though. The overall look of NASA was fine, but the computers depicted were way too modern. Rufus was typing on a plain old late '90s computer keyboard. You could see it was the standard modern 100% layout. They didn't have anything resembling that at the time. And the screen they showed looked more like '80s DOS, it even mentioned shortcuts for the F keys, and standard IBM PC drive labels. Also half of their technobabble was gibberish.
And also incredibly lucky for Flynn that his half brother died at the exact same moment as the moon landing! Changing his own mother's history to now include having a kid seems like an insanely stupid risk of wiping himself out of the timeline, given that she met his father as a widower working for a company overseas. A little bit harder to have such an important job and meet a dude with a kid isn't it? Pretty dumb move, and also a coincidence that she appeared to be related to the story. It's also one of my biggest peeves with time travel fiction of changing people's history, but the kids are still the same people. I've only seen one time travel movie even address this point correctly.
Also, they definitely broke their own rule of time travel in this one. I guess it was more of a serving suggestion than a rule, but that would open up even more problems.