This depends a lot on what the ESL student's native language is. Students who speak Russian, for example, have a lot of trouble remembering to put articles in front of nouns. Those who speak Spanish have more trouble with double negatives, both because many Americans speak that way and because double negatives are grammatical in Spanish.
One problem that I have noticed is uncertainty about when and where to use articles such as "the," "a," "an" and so forth. I have noticed this particularly in working with Korean students. It may be that such words do not exist in some languages.