"Shotgun argumentation" is a methaphor from real life: It's much easier to hunt a rabbit with a shotgun than with a rifle. This is because a rifle only fires one bullet and there's a high probability of a miss. A shotgun, however, fires tens or even hundreds of small pellets, and the probability of at least one of them hitting the rabbit is quite high.
Shotgun argumentation has the same basic idea: The more small arguments or "evidence" you present in favor of some claim, the higher the probability that someone will believe you regarldess of how ridiculous those arguments are. There are two reasons for this:
Firstly, just the sheer amount of arguments or "evidence" may be enough to convince someone that something strange is going on. The idea is basically: "There is this much evidence against the official story, there must be something wrong with it." One or two pieces of "evidence" may not be enough to convince anyone, but collect a set of a couple of hundreds of pieces of "evidence" and it immediately starts being more believable.
Of course the fallacy here is that the amount of "evidence" is in no way proof of anything. The vast majority, and usually all of this "evidence" is easily explainable and just patently false. There may be a few points which may be more difficult to explain, but they alone wouldn't be so convincing.
Secondly, and more closely related to the shotgun methapor: The more arguments or individual pieces of "evidence" you have, the higher the probability that at least some of them will convince someone. Someone might not get convinced by most of the arguments, but among them there may be one or a few which sounds so plausible to him that he is then convinced. Thus one or a few of the "pellets" hit the "rabbit" and killed it: Mission accomplished.
I have a concrete example of this: I had a friend who is academically educated, a MSc, and doing research work (relating to computer science) at a university. He is rational, intelligent and well-educated.
Yet still this person, at least some years ago, completely believed the Moon hoax theory. Why? He said to me quite explicitly that there was one thing that convinced him: The flag moving after it had been planted on the ground.
One of the pellets had hit the rabbit and killed it. The shotgun argumentation had been successful.
If even highly-educated academic people can fall for such "evidence" (which is easily explained), how more easily are more "regular" people going to believe the sheer amount of them? Sadly, quite a lot more easily.
Most conspiracy theorists continue to present the same old tired arguments which are very easy to prove wrong. They need all those arguments, no matter how ridiculous, for their shotgun argumentation tactics to work.