We have the same HDTV set that you have. Picture quality varies enormously, but it's for the most part NOT the set's fault. Here are some of my observations. Note that I've had a satellite dish and currently have digital cable.
1. Digital cable signals vary in quality not just from one cable provider to another, but from one channel to another. I've seen very good cable (standard def, i.e., digitized NTSC) signals and very poor ones. Cable has had a problem in this regard and so does the industry.
2. NTSC is "low resolution" in the hard specs but a lot of electronic circuitry in modern analog sets (e.g., comb filters and the stuff concocted by Farouda Labs) has done wonders to clean up the image and make it look better than it ought to. Modern NTSC analog sets take advantage of this. But also: Their interlace scanning mode (which is a sort of engineer's trick to double apparent resolution by using an afterlgow effect) can really produce a nice picture -- apparently better than it is.
3. Your eyes are tuned to NTSC and analog, after years of watching same. LCDs and digital images in general will look harsh or strange even if they're superior to the same image in analog and NTSC. This effect will lessen over time.
4. As someone else noted, just because it's digital doesn't mean it's high resolution. Your set CAN display 720p digital resolution, which is low-end high def. It's in between what a good DVD image can offer and what high-end (1080p or 1080i) HDTV provides. Perfectly good for many video sources. It outruns a standard DVD image. [By the way, a couple of the broadcast networks now send their primetime schedules in 1080p, while ABC offers 720p. I can't tell the difference because the Sharp only interpolates to a max of 736p, but all those signals look good to me, here. See more, below.
5. In just a couple of years, sets that offer less than 1080i resolution will be mundane, but for smaller sized sets, that is effective overkill, because unless you sit up real close, you can't discern the additional detail in most cases on a smaller set. If you have a 40 incher, well, ya, 1080 of any kind usually looks better.
6. Eventually, all TV signals in the US will go digital. That doesn't mean they'll go high def. A regular analog TV channel can hold one high def signal or half a dozen standard res digital signals. Some stations are mixing and matching. In bigger cities, like Milwaukee, where I live, we have about 20 over the air digital TV channels right now. The number of HDTV channels among them is never more than half that, sometimes less. Many communities don't yet have stations broadcasting in high def, but that will change. An ordinary TV antenna (on the roof if you're a fringe viewer or rabbit ears if you're close to the transmitters) will pull in those HDTV signals and on my set, which is your model, the picture looks fantastic.
7. I have standard def cable because I don't feel like paying a premium for high def service, which only offers a few channels anyway. So I attached an antenna (in my case, amplified rabbit ears) to the TV input of my set. The cable goes into one of the component inputs alongside the DVD/VHS deck. I switch to broadcast when I want HDTV. At some point, there simply won't be premium charges for high def service, because that will become commonplace.
7. If you want your set to show you the widest array of great high def images, that would mean getting a HDTV satellite dish. At least in the near future, satellite services will offer more HDTV channels than all or most cable providers. But satellite is out for you. One alternative is to buy a Blue Ray or HD-DVD player (pricey at the moment).
8. LCD sets don't particularly handle high-speed motion or very dark images very well, and this is just the way things are. You can tune your set's brightness and contrast to minimize this, but until LCD gets faster and better the artifacts will be visible in some programming (usually appearing as pixelation in darker spots or fast-moving portions of the image).