Continuity: Gertrude asks Lord Goring to accompany Mabel to the art exhibit, and then asks Mabel if she minds. When Mabel replies, you can see the reflection of Gertrude in the mirror behind Mabel. But you shouldn't be able to see Gertrude since she is seated during the entire scene.
Anachronisms: At the reception at the Chiltern's home, Sir Robert is requested to meet the Indian Ambassador. In 1895 India was a British possession and there could not be such an Ambassador who represents only independent states.
Crew or equipment visible: When Arthur's father arrives just as he is leaving for the art exhibition, the camera hits a large vase of orange flowers as it moves to the right, causing them to flutter and move.
Continuity: Lord Goring's jacket is buttoned, then unbuttoned, then buttoned again as he explains Lady Chiltern's letter to Lord Chiltern, Mabel and Lady Chiltern herself near the end of the film.