One of the most common uses of reported speech is to ask for clarification or correct someone: "I thought you said..."
This activity gets students to do just that by having the teacher tell a silly story that contradicts itself. A sample story is included along with notes on how to do the activity. You are welcome to steal my story or write one of your own.
This can be done orally with students interrupting you or as a written exercise. It could even be a fun dictogloss with students assembling the story and then finding the "mistakes".
One of my individual activities for teaching reported or indirect speech. Buy them all for the discounted price of $9 total at: What Did you Say?: Fun Activities to Teach Reported Speech, a 22 page book of activities and ideas of teaching reported or indirect speech.