My favorite is when it bounces back and forth between the same two wrong answers, each time admitting that the most recent answer is wrong and going back to the previous wrong answer.

Doesn't matter if you tell it "that's not correct and neither is ____ so don't try that instead," it likes those two answers and it's going to keep using them.

Once the context is polluted with wrong information, it is almost impossible to get it right again.

The only reliable way to recover is to edit your previous question to include the clarification, and let it regenerate the answer.