Everyone does not have the right to have his opinion taken seriously. In order to have an opinion about something that should be taken seriously, for example, it is a necessary condition that you understand the thing about which you are going to express an opinion. --from ConsiderTheSource
So I'm in a building. Nearby a shot rings out. The macaw next to me squawks: "Duck!".
"What do you know?" are my last words.
A much better notion might be to consider all opinions, regardless of source. See whether they hang together, see whether they are looking at forces you have ignored. See whether, even in their abject stupidity, they give you a better idea.
This seems painfully inefficient to me. As an extreme example, it's like letting the 1000 monkeys bang away at typewriters, and saying 'There might be something good coming out of that.' Sure, there might be, but time and attention are finite, so you're better off having some kinds of filters.
As to your example, obviously you're better served by reacting to gunshots and not to what a macaw might say.
There is a great deal of compromise available here. You shouldn't reject an idea simply because it comes from a less-than-reliable source, for to do so is fallacy. However, you should also not seek ideas from less-than-reliable sources; if you want a good idea, you don't ask a thousand monkeys... you ask an expert. Between these two, it only means you should ConsiderTheIdea after it is brought upon you by circumstance (regardless of the source), but should ConsiderTheSource when making a decision as to where you should seek and find ideas. This is not at all inefficient.
Even a blind pig finds an acorn once in a while.
Out of the mouths of babes, ofttimes come gems.
Related:
Also known as DontBlameTheMessageForTheMessenger