It's a variation of "red-eye" due to the flash being too near the lens. You need to get a larger flash for distance shooting and get it up on a bracket to get it up away from the camera. That way the light from the flash doesn't reflect off of the retina straight back at the camera.
To fix these photos, many photo editors can correct "red-eye". Not sure if Picasa does, but it's a free photo editing program.