Not sure if it’s an urban myth but I’ve heard it said more than once that the total computing power of the Apollo 11 mission was comparable to a ZX spectrum.
[nerd]
It’s true that the guidance computer didn’t have a lot of RAM and memory, but then it had only one function: take readings of stars (in putted by the astronauts) and work out where they were, so it didn’t really need much in the way of processor power or speed. it did however have a 00404 error mode….
[/nerd]
The computer was cutting edge at the time, but as nickc says, didn’t need to do much. it was, however, pretty reliable and fault tolerant. It knew when it was getting overloaded (like during the first moon landing) and alerted the crew. It was able to be reset and pick up where it left off. (And the moon landing wasn’t manually flown by Armstrong, just not fully automatic.)
(The cause of the overload is pretty interesting if you’re really nerdy.)