The cable companies only allocate so much bandwidth to each of the HD channels. With MPEG2 compression that bandwidth may not be enough to transmit all the detail in the original source as they receive it. In my experience this only becomes noticeable in relatively extreme cases with lots of detail that is moving.
Other times the compression artifacts have clearly originated upstream of the cable company. For example, the "Star Trek - The Next Generation" episodes aired on "Spike" have horrible compression artifacts that were noticeable even with analog cable on my old 20" 4:3 CRT. Mostly noticeable as motion glitches, where character's movements appeared a little strange.
There's another thing to consider. When you're watching a DVD, that's also MPEG2 compressed. But in high-quality DVDs, considerable time can be spent optimizing the MPEG compression parameters for each scene. For live broadcasts, or for digital cable, the re-encoding to MPEG2 is done on the fly and is not optimized for the type of scene on the screen.
Have you noticed the quality of live HD broadcasts vary greatly? Lighting may be a big part of it. Some sports broadcasts appear very muddy and murky and lack the crisp detail you expect with HD. Others are very good. The late-night shows with David Letterman and Jay Leno in HD look absolutely fantastic (but aren't generally of interest to me).