This is an interesting one that I see from time to time. This fallacy hinges on a previous fallacy. Claiming someone's claim is wrong just because the argument contains a fallacy does not make the claim wrong. I realize that there are currently people who believe that the Earth is flat, but all evidence I have tells me that it is round. Now, if I argue that the world is round because only idiots believe otherwise, it's a bad argument, but not necessarily untrue that the world is round. I have attacked my opponents character, but I have not proven that the initial claim. Scientifically speaking, it may be a proven fact. It may be frustrating to me that people deny and doubt science. That does not mean that my argument that contains a fallacy is inherently false.
Some people will say that since I said something that was logically false (only idiots believe...) that my whole argument is wrong. You may have a harder time believing my claim when I use logical fallacies, but that doesn't make it untrue. I am guilty of this sometimes as well. If I see someone unable to form a coherent sentence trying to tell me something about language, I won't believe them until I hear it from a more credible source. I sometimes make grammar mistakes, even as a person with a master's degree in English, but I try to at least sound coherent. We need to stop and argue credibility rather than false claim when an argument contains a fallacy already. Rather than say that the world is flat because my claim that only idiots believe it is flat is a fallacy and therefore it cannot be round, we need to say that because the claim contains a fallacy, a new argument must be made without a fallacy. The argument is weakened due to the fallacy.