Any camera that has the flash that close to the lens can and will give you red-eye if you shoot images of people in a darkened room. You can get red-eye with a $5000 Nikon camera as easily as a cheaper point and shoot
The way to cure red-eye is to get the light away from the lens. This in itself presents a problem when your using a point-n-shoot type of camera. One option that you may try it by either only shooting in areas where you have plenty of light to shoot - instead of using your flash....or by bringing in some additional tungsten lighting, setting your white balance to tungsten/indoor lighting and using that light instead of using your on-camera flash. Either of those two situations will yield great results without red-eye.
Here's the low-down on red-eye. When you shoot a picture of someone in a darkened room, their pupils are opened 'way up' so as to let in light into the eye - so their eyes can focus. Just as...when we go outside in bright light, our pupils automatically get smaller - as to control the amount of light coming into the eye. OK - back to shooting indoors in a darkened room......because the pupil is opened up so much to let in more light into the eye, the back of the eyeball is easily accessed by your flash. And...the back of the eyeball happens to be RED. So, you aim your camera at a person in a darkened room - their pupils are very wide - you snap the pic and the light from the flash not only lights up your person but it also lights up the back of the eye - and that's where you get red-eye from...
That'll be $200 please
Dean*