a lot of cameras have a red eye option, but they just don't work very well. Red eye is a problem with compact cameras because the flash is so close to the lens.

Some color eyes are more prone to red eye then others...my brown eyes hardly ever have red eye, and my wife's blue eyes always get red eyes.

My cats get really bad glare from the flash. Don't know about dogs.

The best way to get rid of red eye is not to use the flash