In order to critique the interpretive and analytical preciseness of a written piece, you must first look into what exactly they are interpreting. This can be accomplished first by reading quotes and information listed within the article and then by checking the sources to ensure the data is accurate and comes from a trustworthy source. Be sure that all quotes are taken within context, as writers who take information out of context either misunderstood the article or intend to mislead their readers. Also be sure that the information is current, or at least relevant to the piece of writing.
Good writers are able to show more than one viewpoint and still draw a definitive, logical conclusion. Thus, any good informative work should draw from a variety of sources in order to provide the reader with more knowledge and to exercise their own interpretive and analytical skills. They should also be able to show logistical flaws when citing works they disagree with. More importantly, they should be able to read between the lines of their cited works. Imagine an article based on Jonathan Swift's "A Modest Proposal" that contemplated the economic validity of cannibalism rather than examining the Irish famine or upper-class bias at the time. Good writers are also good readers; if they don't get the point of another person's article, chances are they aren't very good at writing about it.
Precision comes with details-- the smaller, the better. Writers who write in generalities might delight their readers, but they wouldn't be able to discuss their topic with much precision. Think about the difference between saying, "Witch hunts usually targeted women" and "German Inquisitor Henrich Kramer's 1487 witch-hunting manual Malleus Maleficarum includes several passages that indicate Kramer's distrust of female sexuality, which he equates with witchcraft." The former example could apply to any time period or any culture, and doesn't indicate why women were targeted, whereas the latter answers these questions and implies that passages from the text itself will be discussed. Writers should narrow the scope of their work and aim to find as many details as possible to support their conclusions.
The writing itself should be engaging, but it should not attempt to use emotion or exaggeration as rhetorical devices, no matter how passionate the writer is about a given subject. There should be a clear organizational structure, whether it be chronological or thematic. If the topic at hand contains unfamiliar vocabulary, these terms should be identified and defined as they apply to the article. Keep in mind that amateur writers may attempt to use logical fallacies to prove their point particularly by referring to authority ("Einstein said ___, so it must be true"), or by making generalizations ("It seems that humans are just inherently selfish"). Be prepared to point such errors out to the writer to show that your criticism is founded and to help them improve for their next writing task.