I’m applying to a masters program and I need to find a potential advisor prior to applying. I’ve heard that it’s a great idea to reads some papers from the potential advisor and make thought-out comments on the papers when contacting the advisor(s) to show that you have genuine interest in their research. I am awful at thinking of questions / interesting comments. Although it would be impossible for you to suggest what I should mention about the paper without having read it, what areas of a research paper should I focus on when making insightful comments about it?
It's good to look into a potential advisor's research. If there is a specific reason you are interested in working with them, that is also good to mention that (briefly) in an initial email.
However, I think making detailed, specific comments about the professor's papers would usually be a bad idea in this context. It is far too much detail for an introduction, and if you are doing it just to demonstrate your knowledge and/or interest, it will come across as forced and artificial. If someone was advising you to do this, I don't think it was good advice.
Keep the initial contact brief: introduce yourself and say something about why you want to work with them.