Correction, editing, and sentence-level grammar are of very little intrinsic interest to me. These tasks are considered, rightly, the final stage of the writing process. Think of it as the clean-up phase that comes long after inspiration, invention, creation, production, etc. In other words, only appropriate when the words you're mostly happy with have already been created. Too many writers, however, focus on this step in the writing process, which has the effect of truncating their thoughts. Now, thoughts, from my perspective, are precious commodities. They are the hardest part to come up with. Invention of a new thought is one of those things I take very seriously, and adamantly resist any force that comes close to interfering with it.
The clean-up phase requires a fair amount of attention to detail, but it also attracts obsessives and perfectionists. There is a mentality that focuses on error that is positively annoying, but it's also dangerous for some students, especially those who are marginalized. Mina Shaughnessy's Errors and Expectations
Correcting error is a tricky path to walk. It is extremely difficult to correct someone without employing criticism, or implying the other is a flawed being. Very few people are so self-confident that they have learned how to ignore the psychological and emotional affect of having been corrected. Most people feel it very keenly, and if the act of criticism is handled badly by the person in power who is authorized to do the correcting, the person who is being corrected might shut down completely and stop writing entirely. There is no error that makes taking this risk with a student's creativity worthwhile.
How right does the error-corrector need to be? Writers need to know when they've made a mistake, yes. However, there are people who correct writing who carry this need to convey wrongness to extremes. Think about the effect your need to be right will have on your student, or on the basic writer—or even on the published writer who is, nonetheless, insecure. The quest for perfection, and forcing correctness on others (especially students who cannot defend themselves, due to the inherent power imbalance in the student-teacher relationship) is redolent of the Victorian era, when the English dominated the planet and were allowed to tell everyone, in judgemental tones, how to conduct their business. I keep wondering when students will rebel against this treatment.