There are a number of problems that pronouns can present for writers, but two are especially common: agreement and case. We’ll take agreement first.

Pronoun-antecedent agreement

You know that subjects have to agree with verbs. Well, pronouns have to agree, too. They have to agree with the nouns that they replace and to which they refer. Those nouns are called antecedents; they are the words that appear first and are then replaced by pronouns. For example, if you’re talking about Patrick, and after a while you start referring to Patrick as he, then Patrick is the antecedent, and he is the pronoun that takes the place of it and refers to it. Patrick and he agree because they are both singular. You also have agreement when both the noun antecedent and the pronoun that replaces it are plural. You have disagreement only when one is plural and the other singular. Here are examples of the error of pronoun-antecedent disagreement. Correct 1 through 3 to make the antecedents and the pronouns agree in number:

1. The mailman came late, but they always do on Mondays.

2. A student is very fortunate if they have a job waiting for them after graduation.

3. All the vetoes were in, but it didn’t add up to a clear picture.

It’s really very simple. Singular pronouns agree with singular nouns. Plural pronouns agree with plural nouns.