The most extraordinary part of putting man on the moon or even just high earth orbit has to do with the hostility of the environment. Most of the rules of ultrasonic flight had already been somewhat mastered by 1969. The computer power part of it is almost irrelevant. Launching, not much of an issue. Launching = size matters. Every seen the Saturn V rocket in Houston? Yeah, sure. You have to be nuts to take the seat on a giant firecracker. Its nothing but a huge fuel tank. Escaping earth's orbit just takes a lot of energy. Don't let size be comparable to complexity because the rocket engines were just an evolution of the missile engines already in use at the time. Most of the body of the rocket would disappear in the atmosphere so they don't even have to bother to design it to withstand space for long. Just like a regular airplane must dump its fuel if it needs to make an emergency landing, because it was not structurally designed to withstand such landing.
Landing on the moon? Well is a lot easier to land on anything if you don't have to worry about weather and if you don't have to worry about gravity screwing you if you make a mistake. I know so because I use to fly gliders for sport and trust me, gravity and weather are far worst than elders when it comes to forgiving.
Now please don't get me wrong.. I am not saying that the above is achievable by just anyone. As you can see there is only a few very rich guys who have attempted at building something somewhat close to a spaceship. What I am trying to do is put the flight itself in perspective with the other challenges of space travel, which are much bigger. There are lots of issues, from safety, to hardware reliability (sorry, no spacecraft parts stores up there). For example, there is a certain area over the atlantic where computers begin to generate bit errors on memory, due to a certain type of radiation present there. This is more of an issue with orbiting spacecraft but it exemplifies what I mean. Computers have to be certified for space flight before they are chosen for mission. It is said that the this same anomaly causes astronauts to see bright spots on front of their eyes for a short period of time. Managing changing temperatures is another big issue. Astronauts often get burns, even with protection, as a result of handling tools and parts in space. The cockpit of the space shuttle is attached to the rest of the aircraft at only for anchor point, to help isolate heat from the cargo bay. This is the reason that the cockpit is seen tumbling apart from the explosion during the challenger incident. Reliability of the hardware is another big issue. Just like in airplanes, 90% of the dials and knobs you see are redundant of one another. Provided that a spacecraft has more controls than an airplane. Point being is that the minimum items required for flight are usually much more less than what you see in pictures. The rest is there for safety, redundancy and unforeseen issues. An airplane is quite similar in that respect. Airplanes can safely be flown (I've said safely, not comfortably) with just an altimeter and a airspeed indicator. If the weather is good enough and you have visual of an airport you are familiar with, the altimeter is almost useless ( I said "almost"). The airspeed indicator is what keeps you flying.
An astronaut must undergo a lot of training. The only ones that get to fly the craft are usually ex-military with previous flight experience. As in any other situation, there is adaptation time that they need to put in in order to get to know the aircraft, especially one as heavy, but they spent quite a lot of time training in safety. They are trained on landing the shuttle by taking a Gulfstream Jet, flying it with the rear landing gear down and the engine in reverse trusters. One heck of a flying brick if you ask me. How to respond to unforeseen events, spacial orientation, etc. In modern times, most of the training is also put on the actual goal of the mission (like repairing the Hubble), not on just getting to orbit. I can't remember the name of the fellow, but there was a space station astronaut (not the ISS, an older one) who went to sleep one night while in space. He woke up to find out his bed straps had become loose and he was floating in the middle of the craft, with no way to reach either side of it. He immediately panics because he doesn't know how to move from where he was. Good thing he was not sleeping naked.
I was going to open this paragraph saying "As you can see" but I don't want to sound like there are no holes in my narrative. I just hope that I made the big picture clear enough. I am a mechanical engineer by education but never got to actually do much in the field. I am in IT at present. Off course, to a rocket engineer, everything he does is simply common sense. So do not let your own "common sense" define your facts. I am willing to be corrected because I am not trying to hold a technical discussion here, I am just trying to contribute to the discussion.
If, in the other hand, we are going to consider the possibility of a hoax. Remember, no black and white thinking. If it was a hoax, not the whole thing had to be a hoax. If it is not a hoax, then not the whole thing had to be true.