In this category, you'll notice something else that you may have noticed in this painting. Obviously, this painting was not created for the film. The Fighting Temeraire was an actual painting, even a famous painting, before this movie. This artwork requires a little analysis because its nature in the film is full of symbolism.
So, I'm going to cover the painting first. The painting is by the foremost of the Romantic British Painters, J.M.W. Turner. It was painted in 1838, as the rotting warship was taken off to be scrapped. The HMS Temeraire was a fairly notable ship that appeared in the Battle of Trafalgar (enjoy the painting by Clarkson Frederick Stanfield).
Now, how does it relate? In Skyfall, a major theme is Bond's fear that he is unneeded, that the MI6 is an old tradition that is on its way out. In the beginning of the film, these repressed fears plague Bond.
An important thing to remember in film is that everything is done for a reason. The scene is an enjoyable scene without knowing anything about the National Gallery, about Turner, about The Fighting Temerarie. But of all a sudden, when you realize what the painting portrays, what it represents the scene becomes powerful. Bond's fixation with the painting shows his fixation with his repressed emotion. He likens himself to the warship, he fears he has become a part of British tradition, gone to rot.