Not all of these considerations are applicable to every secondary source: but here’s a list of things you could look out for or research, in addition to your own response to the content of the article and the argument it puts forward. Some of them will be dead ends, while others might lead to a profitable way of looking at the book/article.
Author: other publications, background (literature, archaeology, economics etc), critical reception (reviews of other published work).
Audience: which journal is this published in, and what is the journal’s stated agenda and audience? Is it aimed at a purely scholarly audience? Is it interdisciplinary? Does it have a particular focus (women, reception etc)?
Year of publication: when was this published, in relation to other work on the same subject? Is it influenced by contemporary scholarship? What has the author published since?
Scope: what are the limitations of this study? Would a wider scope give a different outcome?
Theory/methodology: what does the author say about his or her approach to the subject? Are there underlying assumptions (shown, for instance, in choice of terminology or research methods) which are not explained by the author?
Citations: Google Scholar is good for this. Look at the list of works which have cited your article. How influential is it? How is it used by other scholars?
Classical Studies Support 