Read the introductory paragraph, and identify the thesis statement. The thesis statement serves as a concise summary of the research paper's argument. Thus, it is important you understand the thesis statement so that you can ensure the paper fulfills it. Check that the thesis statement is direct and easy to understand, even if you are unfamiliar with the subject matter.
Read the first sentence of each paragraph. These sentences should serve as topic sentences and support the argument set forth in the thesis. Ensure that each topic sentence relates directly back to the thesis and does not stray from the writer's central argument.
Make note of transitions as you read. Each paragraph should flow into the next, even as the writer shifts the focus of the paper. If there are any paragraphs that lack transitions, make note of it in the margins of the paper.
Review the content in each paragraph. The content of each paragraph should relate to the topic sentence. Ensure that each paragraph offers rich content with detailed research from credible sources. Paragraphs should offer a mix of research -- such as paraphrased content and direct quotes -- as well as original thoughts by the writer. If a paragraph lacks substance or relevant research, note it in the margin.
Review the organization of the research paper. If the writer seems to jump back and forth between topics, tell him. If you have trouble following the paper because it is poorly organized, offer suggestions for better ways to organize it.
Keep track of any recurrent grammatical issues in the paper. You aren't the copy editor, but if you see ongoing grammatical problems, the writer needs to fix them. Mark these grammatical errors as you see them, or write up major issues at the end of the paper or in a separate document.
Look out for any questionable content. If the writer appears to be passing another source's content off as her own -- or you suspect she is -- then query that content. Perhaps she forgot to include a parenthetical citation. Your comments can help her avoid plagiarism, even if it's unintentional.