Let me guess: It looks a lot like this:
That would be what the "i" in 480i means. Interlaced. It essentially displays two separate images, alternating line by line. It's a method to reduce the amount of bandwidth required to display motion video, and since most CRT/non-SD TV's are tuned to actually display this way, it worked for a long time and nobody really noticed it. Now that we have LCD's and HDTV's, the method for displaying images on a screen have changed. Instead of alternating each line, the entire screen is updated on every frame of video, which means that you'll be seeing those "half-images" and flickering from sources not designed to be displayed "progressively" (the "p" in 480p). Most modern HDTV's have what's known as a "comb filter" to combine the half-images over time and increase picture quality (and usually perform some image processing to clean it up), but cheaper sets still tend to not include this (mostly-standard) feature.
The PS2 is capable of outputting 480p (and I believe in some games higher), but only with games that support it - Otherwise, it will default to 480i and you'll continue to get that ghosted image. There isn't any way around that.
Sort of, only the two were just one or two pixels apart, it's there even when the image isn't moving.