Here is a sentence that has an error, but not many people catch it: "Each student is responsible for cleaning their locker or they will be fined." Student is just one person whereas their/they means many people; in other words, student is singular and their/they is plural. When we speak, we commonly use they and their to refer to an individual if we mean the person could be either male or female. In English we don't have any gender-neutral pronoun other than "it" and we don't want to call any person an it. So we might say aloud "A child might miss their bus in the morning if the bus driver is early" because we don't want to assume that the child is male or female. The problem is that in written English, using they/their to refer to one person is--for now--inappropriate. It's a rule that drives me nuts, but alas we have to fix our they/theirs by doing gymnastics in our sentences to sound proper. Here are corrected sentences:
Each student is responsible for cleaning his or her locker (stays in the singular) or must pay a fine (rewritten to avoid they).
Students are responsible for cleaning their lockers or they will be fined (converts the sentence into plural).
A child might miss the bus in the morning if the bus driver is early (avoids their and uses the).
A child might miss his/her bus in the morning if the bus driver is early (ugly but acceptable in the singular).
Children might miss their bus in the morning if the bus driver is early (makes the subject plural).
