Ask any grammar buff about agreement, and chances are she’ll talk your ear off. She’ll tell you that verbs must always agree in number with their subjects. She may even tell you about some of her own agreement-related peeves, like how people sometimes use a singular verb with a word like “data,” which in the strictest sense is supposed to be a plural. In other words, you’ll get an earful on subject-verb agreement.
It’s also possible your grammar aficionado will go off on a tangent about “pronoun-antecedent agreement” — the scary-sounding name for the very simple idea that plural pronouns should stand in only for plural nouns and singular pronouns should stand in for singular nouns. These are tough times for proponents of that rule, as grammarians become ever-more accepting of “they” and “their” referring to singular things. For example, “Every patron should be sure their car is securely locked.” Traditionalists say that because “patron” is singular, you can’t use the plural “their” here. Others say that “their” is a good way to avoid the clunky “his or her.”