Here are some questions that can help you judge the effectiveness of an argument:
What conclusions about the argument can you reach by playing both the believing and the doubting game?
What cultural contexts inform the argument, and what do they tell you about where the writer is coming from?
How has the writer established credibility to write about the topic?
What reasons and assumptions support and underlie the claim?
What additional evidence backs up the assumption and claim? How current and reliable are the sources?
How does the writer use images, graphics, or other visuals to support the argument?
What fallacies can you identify, and what effect do they have on the argument’s persuasiveness?
What is the overall impression you get from analyzing the argument? Are you convinced?