It might depend on the dog, but television is geared to only work with human eyes. If an animals eyes are advanced enough, they would see the TV for the LED's rather than the projected image. Also, TV's work by blending three different colors to create an image that imitates what a human might see within their perceptual spectrum. The dog may be able to see more or less of these colors. I know that dogs see more blues than humans, whose eyes tend to center on yellow-green light. Seriously, paint your car a bright yellow-green and see how many people notice you. Anyways, this could mess with their perception of the image on the TV screen, as well. That doesn't mean the same is for all dogs, or that dogs can't still see an image. I'm just saying what they see is different from what we're used to. Our minds aren't designed to process in terms of a dog's senses, so we can't really imagine what they'd see.
I'm also fairly sure that a mirror isn't a 2d image, and I know that animals can see those. They're just smart enough to know what they are (usually)