Welcome to my world. I've been upset for quite a while now on the quality of HD video, which has actually gone down since I first got set up in 2004! I spent a lot of money upgrading my equipment so I expect to get better quality video than what we're getting. Quite a lot of times the quality is so bad I think I'd prefer an anamorphic DVD.
I see compression artifacts on all HDTV channels, OTA or on Dish. Its just a matter of over compression. OTA TV uses MPEG-2 compression, each ATSC channel has about 19Mbps of bandwidth, which is enough for pretty good video quality. 3 of the 4 major networks (what you see ota from FOX is what FOX's headend sends out) use a system in which they deliver a very high bandwidth signal to their affiliates, which in turn re compress it to fit into one ATSC channel. The problem is many stations don't use their entire bandwidth for one channel, they want to cram in an SD (or sometime an HD) subchannel for a bit of extra revenue. That severely degrades the picture quality. Another issues is, for some reason some of the stations in my locality don't use their entire bandwidth. CBS(KRQE) here broadcasts at 17Mbps even though they have no sub station.
Dish uses h.264 compression which is much better than MPEG-2 but they're cramming in 8(!) HDTV channels per 40Mbps transponder. Thats roughly 5 Mbps per channel, which isn't anywhere near enough for 1080i. For comparison, Blu-ray discs generally average around 30Mbps or more for video. As far as your locals go, by the time you see it on Dish the program your watching has already gone through compression at the network, then again at your local affiliate, then yet again by Dish. Dish's HD locals look much softer to me than from over the air.
I have two ways of watching HD. One on my 42" 720p Panasonic plasma. Some channels from Dish look OK on it, others are pretty much unwatchable. The other is a 24" Dell Ultrasharp 1080p monitor, pretty high end. I can't hardly stand watching Dish HDTV on it when sitting at my desk. For some reason Plasma TV's do better than LCD's with poor quality HD, also 720p sets look better as well, someone else smarter than me can probably explain why. You also need to take into account your viewing distance versus the size of your TV. I'd suggest turning your sharpness all the way down, and tweaking the contrast down some as well.