Reading Common false beliefs in Physics I feel that there are also "fake false beliefs", ie, that the "false belief" does not actually exists, it is a rhetorical argument or just a basis for argumentation, but not actually a belief... while the meta-belief on its existence actually exists.
Prototypical example is mid-age "flat-earth". All the discussion with Colon was about the diameter of the earth, not about the flatness or sphericity. And still, you can hear here and there that the mid-age philosophers had the "false belief" of a flat earth.
A more dubious example: does people actually think that summer is related to the distance to the sun? Or is it a rhetorical trick of the teacher, to induce this thinking during the classroom only to correct it later? Most countrymen clearly perceive that summer is about height of the sun, not distance.