The major advantage of DVI so far as most consumers are concerned is that it means the display doesn't have to guess how to display the signal - it will always know exactly what resolution it's being given and when you run it at native resolution this means it can do an exact 1:1 mapping of the pixels.
This means you don't have to press auto adjust, the image doesn't tend to wander over time as the signal gets out of sync, and you don't have to worry about what your desktop image is
Finally, as DVI is a digital signal rather than the analog signal VGA provides, what you see is an exact copy of what was sent. Colours are as 100% accurate as the display can make them and there is no possibility for interferance on the cable to mess with the image quality. This is more important for people who work with images (digital artists, photographers, graphic designers etc) but it's still an advantage.
Whether you personally see much of a difference largely depends on both the quality of the DAC (digital to analog converter) on your graphics card and the ADC (you can guess that one!) in the monitor. These days they can be pretty accurate, but using DVI eliminates the process of converting the signal to analog then back to digital for display so keeps the signal "pure".
Ghosting is what the response time rating of an LCD is all about. There is a small delay involved in changing a pixel on an LCD to the new value for the current image. On your display Asus claim it's 2ms although frankly that's a little optimisic! Because of the delay, a fading after-image (a ghost) can sometimes be seen. This happens especially in high contrast areas as changing a pixel from fully off to fully on (or vice versa) takes the longest time of all.
I'm not sure what you mean by colour bleed - do you mean backlight bleed? That's where the backlight in the display which shines through the LCD panel to provide the display brightness appears to come around the edges of the screen. No LCD can provide a true black, but on some displays the black gets much worse (i.e. lighter) near the edges as light seeps round. Luckily yours doesn't have that problem from reports on these boards so far.
Hope that helps
