Artifacts in DVD videos are possible but then it's probably badly mastered (bad encoder software or bad settings) just like Audio CDs that can sound great or crappy depending on the production.

Uncompressed digital video is hardly used anywhere. Not even DV - used by digital cameras - is uncompressed:
http://en.wikipedia.org/wiki/DV

If people want uncompressed video, they usually go for analog
formats on film. Most of these have still a higher resolution than HDTV but it's difficult to compare due to the different properties of the media.

Your calculation is about right but a pixel uses only 24 or 16 bits. Video data is almost never stored in RGB format but
YUV (or more correct: YCbCr http://en.wikipedia.org/wiki/YCbCr) - luminance, blue chroma, red chroma. Most uncompressed but reduced video formats use 4 luminance values per 2 blue and 2 red chroma values (called 4:2:2). That's how the 16 bit per pixel are calculated. It's very different from RGB 16-bit formats which would allow only 65536 colors.