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.
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.
Several MPs including Lord Caversham are shown wearing top hats in Parliament. MPs didn't (and still don't) wear hats during a session of the House, unless they are raising a Point of Order while a vote is in progress.
The Speaker is shown calling MPs to speak by naming their constituency ("The Honourable Member for Witney" etc). British MPs do address each other in this way, but the Speaker calls MPs to speak by naming them personally.