Revealing mistake: A straight and level seam connecting the top and bottom halves of the tunnel Spock is crawling through is visible.
Suggested correction: Views of the tunnels made before the creature was wounded by Kirk and Spock appear almost perfectly smooth. It is explained that the creature exudes a powerful acid to dissolve the rock. This tunnel was made after the creature was wounded, so it is logical that the wounded portion of the creature would secrete less acid thus leaving an imperfection as the creature tunnels. This could be a case of incredible attention to detail by the set designer rather than an error revealed.
This correction is too much of a stretch to explain a perfect seam by the wounded Horta. Plus, if the Horta was secreting less corrosive substance, then that area would be less eroded, not more. If attention to detail was paid, then the area would have an outward seam, not an inward one.
Continuity mistake: When Kirk is facing the Horta he has his phaser in his right hand when seen from the front but when seen from behind he has his communicator in his left hand and no phaser. (00:31:00 - 00:38:00)
Revealing mistake: When Kirk holds a golden egg, a seam can be seen on it. (00:43:55)