I noticed something similar on my LCD LN32A550. I have not started troubleshooting my problem yet, so I will be interested to see what people say about your problem. I am using a DirecTV HD receiver, and I noticed it when there were some thin white lines going horizontally across the screen. It looked the same as when the convergence is off on older CRTs. Since it is an LCD, this should be impossible. I do not see the same problem now while using it as my computer monitor, so I do not think my TV is at fault.
How do you have your source hooked up? Since it is an SD signal, is it a cable or satellite box? Make sure you are using the best possible connection your box supports. I would use S-Video or component cables if your box supports it. If you are using the old composite (single RCA for video), or, you are using a coax from a "TV out" and tuning in to Ch 3, your picture quality will be far from the best your TV can give you.
Also, look at the quality of your cables. If the shielding is week, or if there is a slight short between the shielding and the conductor, or cable quality is poor (thin), you will see image quality problems.
The ghosting problem sounds a little like what you can get from analog over the air reception when you get multi-path reception from the station (eg, signal straight from the TV station, and then the same signal after it has bounced off a wall, mountain, etc, causing it to be received slightly later it time). If you are using cable, this could be their fault as they might be using an antenna themselves to pickup the signal.
* First thing I would do is hook up an antenna to the back of your TV and watch some OTA HD channels. I pickup much more HD channels then I could with my old SD TV. This will allow you to see what your TV can do in HD, and will rule out any problems caused your cable or satellite company.
* Second, make sure you are using the best possible output to your TV. HDMI is the best, Component next (3 RCA cables for video), then S-Video, then composite (single RCA cable), then last is coax.
* Try different cables to make sure you don't have a bad cable.
* See if there is a firmware update that addresses your problem. Just be careful with firmware updates and follow the directions to the letter as firmware updates can go very bad. Just look around at this website and you will find a few examples.
Also, one of the draw backs of a good HD TV, is that it will show any and all defects in your source signal. Most, if not all cable and satellite companies compress the video signal to squeeze more channels through. When I had Comcast, the digital artifacts caused by their compression was so bad, that I got canceled it. (and that was when I had an old CRT ST TV). Also, I have never seen SD look good on an HD tv. So, when you get HD, you should notice a world of difference
Good luck! If I track down the cause of my "convergence" problem, I will post it here to see if it applies.