What if I find a mistake in a published article?
I would say it is pretty common to see mistakes/errors in published articles. I am not talking about typos or grammatical errors here but misinterpretation of results. Nowadays, since pretty much everything is done with a pre-packaged software, there is not much room for error in applying a statistical method either. Someone famous (Sorry about my poor memory) once said that regression is the most successful yet most abused statistical method so far. I couldn't agree more. You have to admit everybody can do some analysis, but not everyone can do it correctly.
The best way is to just ignore those articles. Actually, I got this idea from my PhD advisor. He once said that it is not worthwhile to write an article to correct them (poorly conducted studies) unless it is a Science or Nature article. I think it makes sense. Not citing a poorly conducted study is like helping slow down the spread of misinformation especially in a field like ecology, where cross-examination is close to impossible and retraction is rare.
There are two types of potential mistakes, "hard" mistakes and "soft" mistakes. These are the terms one of my high school teachers uses (sorry, I forgot your name too). He said that always try to find "hard" mistakes, serious mistakes that are crucial to the correctness of a statement, not "soft" mistakes, which may or may not be true but doesn't really matter with respect to the validity of a statement. Over the years in high school and afterwards, I have gotten into the habit of simply ignoring non-essential details, and concentrate just on the core idea. A side effect of being like this is that I am not a detail oriented person, which is a nice attribute to have in many situations.
So what if I find a mistake in a published article? My advice on this is to discuss it with your friends and colleagues to see what they think. It could be a false positive sometimes. Either way, try to use it as a learning opportunity and never cite that paper for the sake of attacking it if you are 99% sure it has been poorly conducted. If not, that paper will get a new citation, and people would think this paper is a good one. Let's just admit this: we almost always just read title and abstract but never the full text. People will not realise it is a downvote intead of a upvote most of the times, and may even spread the misinformation more.
Also, don't be so serious.
Anyway, this is just my opinion. I don't think there is a right or wrong answer here, just like almost everything else in real life.