Final answer:
The sentence incorrectly uses semicolons to separate items in a list. Commas should be used instead.
Step-by-step explanation:
The sentence incorrectly uses semicolons. Semicolons are used to join two independent clauses without a coordinating conjunction, to separate items in a list if the items contain commas, or to separate items in a complex series that already contains commas.
In this sentence, commas should be used to separate the characters in the list instead of semicolons. The correct sentence would be:
In Shakespeare's classic play Hamlet, Prince of Denmark, the characters include Hamlet, the prince, Gertrude, the mother, Claudius, the uncle-stepfather, and Horatio, the faithful friend.
Learn more about Proper use of punctuation in a sentence