Lack of agreement between pronoun and antecedent.
Pronouns (he, they, it, etc.) must match their antecedents:
After a physician has completed medical school and residence, they can make a good deal of money.
Problem and cure: The plural pronoun "they" doesn’t agree with (or "match") the word to which it refers (its antecedent), "a physician," which is singular. One would be better off with one of these:
After physicians complete medical school and residence, they can make a good deal of money.
or
After a physician has completed medical school and residence, he or she can make a good deal of money.
Since many physicians are women, the "he or she" is more accurate than simply "he." In some situations, "he" is still accepted as a genderless pronoun, but this seems to be less and less the case.
Some writing teachers accept "they" as a genderless, singular pronoun, but few if any accomplished writers use the word in this way. In all cases it is better to use a singular pronoun for a singular antecedent.