There is nothing wrong with the swan's leg. This is a normal resting position for the swans and some researchers think that this position allows for heat dissipation because of the number of blood vessels in the webbing of the bird's feet, similar to a dog panting which dissipates heat.

The color of cygnets means nothing other than in the mute swans in which a white cygnet is known as a leucistic coloring called "Polish" mute and a taupe or grey colored mute cygnet is known as the "Royal" mute. The Regal Swan