Words of Wisdom
There seems to have been in every period of the past, as there is now, a distinct apprehension in the minds of very many worthy persons that the English tongue is always in the condition approaching collapse, and that arduous efforts must be put forth, and put forth persistently, in order to save it from destruction.
— The Standard of Usage in English (New York: Harper & Brothers, 1908): 1-2.
First, the good news: teaching writing is not teaching the rules of grammar. As a faculty member, you may worry that you are unprepared to teach writing or to correct someone's spoken English; however, as a faculty member you are inevitably a writer and a public speaker, and this is a skill you have an obligation to share with your students.
Share your own brand of expertise. If grammar and punctuation are not your strong points, remark only upon those errors that bother you, those that interfere with your reading or jar your listening. If you are unsure of “rules” (which, incidentally, vary considerably), then don’t weight them as much as those elements you are more confident in teaching.
A note on the lingo: grammar technically involves issues like word order, agreement, verb tense, and the like, but the term is often used to include punctuation and usage.
Usage covers matters of agreement as to how we will use language, often not related to grammar in the linguistic sense, such as whether or not we will use contractions, end a sentence with a preposition, or split an infinitive.
Mechanics usually means issues like punctuation but also formatting (margins, typeface, and so on).
The "rules" in fact are really conventions, that is, agreed-upon or prescribed ways of doing things, either because we have done them that way for a long time (as is usually the case with word order or other issues of grammar) or because someone somewhere convinced everyone else that was correct (as in not splitting infinitives). As a result, we have authorities such as grammar handbooks, style guides put out by editors or professional associations, and grammar gurus (like Grammar Girl or William Safire) that don't always agree.
Nevertheless, if you do not base any of the grade on "grammar," you can be sure students will disregard it. They often won't even bother to proofread. Instead of ignoring it or trying to take on the guardianship of the English language, you can strike a middle ground. First, you can explain that you expect the grammar to be appropriate to the audience (in both speaking and writing). Informal or colloquial styles will sometimes be appropriate, although they usually will not in academic writing. Students will appreciate some examples, too. Do you consider contractions informal? (Notice I use them on this website, even for faculty. In some disciplines, they are even used in professional journals.)
Pay attention to the conventions in your discipline and in the genre you want students to work with, and try to give them some sense of what is expected. Second, agree on what you might note in your evaluation of their work. You can use a basic grammar handbook, a style book for your discipline, or a simple handout like Punctuation, Grammar, Style, & Usage: Twelve Guidelines. This handout briefly reviews the conventions most commonly used in edited American English, and it's simple enough for even the most grammar shy to learn.
Error and Improvisation — Jon Olson, Director of the Center for Excellence in Writing at Pennsylvania State University
UWC Writing and Speaking Guides