Most students don't think about the connection between how they put a final paper together and the impact the "look" of the paper has on a reader. The ubiquity of word processors has exacerbated the problem, moreover, because students can easily fool themselves into believing that because a document is nicely printed, they've done the job of presenting a paper.
Simply reminding students that readers need to trust writers can help you make a strong case for careful editing. Ask about their own experiences as readers. If they read a college newspaper that has at least one typo in every article, do they feel confident about the credibility of the writers? Even if they haven't made a conscious judgment about credibility, students will note that college newspapers aren't as professional as big-city newspapers. Part of that judgment comes from subconscious awareness of errors repeatedly showing up in articles.
Readers who see proofreading and editing errors in papers react in exactly the same ways. These readers are more likely to dismiss the professionalism of the writers, and they are even more likely to question data, evidence, and sources in an error-ridden paper.
Professionals and publishers don't edit simply because they want to give readers clear and easy-to-read texts but because they know that edited work keeps intact the writers' credibility as reliable and professional.