Once you've got one or two categories of the most disruptive errors highlighted, look to see if there are any patterns within these types of errors. For example, you may notice that the student uses coordinating conjunctions (and, but, or, nor, for, yet, so) interchangeably with conjunctive adverbs (therefore, then, however, etc.). They aren't interchangeable in formal, edited American English, but explaining the difference to students is fairly easy. One entire sub-category of error might disappear with a two-minute explanation. Similarly, perhaps all the subject-verb agreement errors occur when the student is trying to avoid "he" or "she" as the subject of the sentence. By trying to avoid an apparently sexist usage, the student keeps shifting from "he" to "they," and the verbs don't always reflect a singular or plural subject. Giving the student 20 seconds of advice about changing the entire passage to plural forms (just use "they" throughout) may fix the problem.
If you're working with a native speaker, you probably can't use words like "conjunctive adverb." Instead, list the kinds of words that fall into a category. Similarly, don't talk about first and third person or you'll see the student's eyes glaze over. Talk about "everyone...he" as opposed to "all the students...they" to get the point across about first v. third person reference and agreement issues.
If you're working with a non-native speaker, you can use grammatical terminology if you're comfortable with it, but be sure you're using it accurately. Don't use formal terminology unless you're absolutely sure you know what the terms mean, and don't apologize if you don't want to use it. Just explain that it's clearest for both of you if you use specific examples, like listing several connecting words of the same category--however, then, therefore--rather than relying on more abstract terminology.