[quote user="professorhat"]Hence a more expensive cable which reduces the signal loss, thus less error correction, gives a better picture[/quote]
Since there are error correction bits in the stream, basically providing redundancy, even if there are occaisional errors in the bit stream, the recieving equipment can detect and correct the errors very easily. This wil be dealt with separately from any of the display and picture processing, and is basically transparent. The bit stream should be corrected in real time and be bit for bit correct, and therefore picture and sound should be exactly as intended.
Where this breaks down is when you get multiple errors very close together in the data (within the same error checking block). in this case even the error correction bits can't acurately restore the stream to be bit for bit correct.
What I meant before was that in practice, multiple errors close enough together to be able to foil the error correction and result in a noticeable difference in picture/sound only really occur on very cheap digital cables which are not really up to spec in terms of shielding and resistance. As soon as you have a cable which is up to spec with apropriate shielding (usually only about £15), the stream should be relatively error free over short distances, and the few errors that do occur should be far enough apart so that the error correction can fix it without any loss in quality. Spending more on a cable may well result in less errors in the bit stream (though I suspect there is very little difference over short lengths), however due to the protection that the error correction in the recieving equipment offers, the actual data that gets fed into the display or picture processor should be the same between a £15 and £60 digital cable 99% of the time. This is the advantage of digital. Remember error correction is not interpolation, it results in recovery of the original data.
Longer cable runs are a different story however, and more expensive cables can definitely make a difference there.