Yup, flash, I looked into the red eye reduction lamp, but indeed, it still shows a tiny bit of red eye. As for the background: our house is not big enough to get an even background that is far enough away to be blurred. Not with my current lenses. I am trying to get me an EF 50mm f1.8, which might just solve this problem, perhaps together with some fabric as a background, if I can get my wife to not beat me up because I hammered some nails into the walls ;-)
Flash? The intensity seems fine to me, but darker background (or a longer distance from the existing background) should help reduce the shadow (which, on the other hand, isn't that bad, I'm just being nitpicky). There seems to be a hint of the feared red-eye effect here; did you look into some light source before taking the shot? It should help.