Revealing mistake: It is not what is seen here that is the problem, but what we don't see on the Hogwarts Express; first on the way to Hogwarts when Harry, Ron, and Hermione are in their compartment talking about Draco, and second, during holiday break, when Harry and Ron are talking about Unbreakable Vows. As the camera faces the large compartment window, we see the scenery out the window, but as the train speeds along, the scenic reflection of the windows opposite it, in the corridor, should be seen but isn't. What is reflected is the light colored wall of the compartment beneath the blacked-out window. The camera filming the shots from this angle is positioned at that window, and to hide the camera/crews' outline, the window was covered.
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Revealing mistake: Harry and Dumbledore apparate onto Professor Slughorn's street, and Harry says "I just apparated, didn't I?" As Dumbledore is answering, ("Indeed. Quite successfully too, I might add.") the shot pans out. Look at Dumbledore's "burnt" hand. The green glove they used to make his hand look blackened is visible on his fingers. It is also visible when he turns and starts walking away from the camera. It is not due to the lighting, as it is not visible in the next shot as they both walk away.