When it comes to identifying the "argument from authority" fallacy, then there is one thing one needs to pay attention to: Is the author using the authority as a source for a fact or for an opinion?
For example, let's take these two statements:
- According to this article from DailyDogMagazine, cats are the worst pets of all.
- According to this article from DailyDogMagazine, domestic cats cause an economic damage of several million dollar each year in form of scratched furniture.
The first is an argument form authority. "It's the opinion of a source I believe in, so it must be correct". This is always a fallacious argument. No source has ultimate moral authority, no matter how much you trust it. You have to check what facts they based their conclusions on and if their chain of reasoning is correct. If you want to convince someone that they are right, you need to prove that you did that work.
The second argument is a source providing a fact. Now the question is whether or not we should believe that fact. Is DailyDogMagazine a reputable source? Are they renowned for providing reliable information based on unbiased research? Or were they caught spreading misinformation or cherry-picking in the past? While no source should always be considered 100% reliable, the past reputation of a source is a good indicator for how much weight their information should have.
Now what should we do if we identify an answer which is based on argument form authority or information from untrustworthy sources?
Downvote it. When readers can not rely on the answer being correct, then "the answer is not useful", just as the tooltip of the downvote button says. You might post one comment where you explain that you downvoted the answer because you don't think it does a good job at convincing you that it is correct.
When you feel that the answer has absolutely no merit because everything in the answer is based on unsourced arguments from authority, you can consider to flag the answer as "very low quality" to put it into the review queue and let the community decide whether to delete it or not. But content deletion should be the ultima ratio. The preferred way to handle bad answers should always be to give the author the opportunity to fix their answer. Deletion should only be considered when an answer contains absolutely no useful content and is definitely unsalvageable.
Regarding comments which try to defend a bad answer by using arguments form authority: It is best to just ignore them. Politics Stack Exchange is not a discussion forum. When someone is convinced of their views, then it is not your job to convert them. It is their job to convince you that their answer is correct. If they fail to convince you, just keep your downvote and move on. Arguing just takes everyone's time and nerves and often leads nowhere:
image source: xkcd