1) It has to map the pixels directly, and not distort the image. For example, a lot of older plasma TVs are actually 1024x768, which is a 4:3 aspect ratio for square pixels, and then stretches the image to 16:9. So, if you feed it a 1920x1080p image, it will shrink it down to 1024x768, and then stretch it back out to 16:9. Not ideal.
2) It depends on how far you sit from it. Older TVs are 1366x768 or 1280x720, but most newer ones are 1920x1080. However, even at 1920x1080, everything will look absolutely enormous on a 40" TV if it's on your desk. What's worse, the pixels and the spaces between the pixels will look huge.
1920x1080 is better suited to a 21" screen if it's going to be sitting on your desk.
3) If it's sitting on your desk and close to you, the top of the screen will be far too tall. Not ergonomic. Get ready for neck or back pain.