Error correction - good, but far from perfect
A number of people have, quite understandably, mentioned error correction.
Afaict, at the time I am writing this, no one has yet mentioned the fact that error correction is not infallible. If things are sufficiently bad, or you are sufficiently unlucky, errors can occur that will not be corrected. Mostly these errors will still be detected, but sometimes they will be undetected and the data that arrives will be plain simple wrong AND (at the digital level) NO ONE WILL KNOW. This is an inevitable characteristic of most error correcting codes.
In a pure-digital setup where the numbers are not representing an analogue quantity, you typically give up and do a retry at that point.
In a mixed A-D-A setup, it is theoretically possible for a design to attempt to guess the missing data e.g. by interpolation from the preceding and following samples (or some other digital or analogue filtering magick). I don't know if that happens in practice, but it's conceivable. Anybody know for sure?
Anyway, this real world digital kit that's so perfect, what does it actually do with an error that it has detected but not been able to correct? Just ignore it (see link below) and rely on filtering/interpolation, hoping that no one will notice?
Are there counters anywhere that keep track of corrected and uncorrected errors on the link?
Your $20 DSL modem/router has the relevant counters and plenty of geeks (sorry, people) know how to use them. It also has the ability to request a retransmit (via the IP protocol).
Setting to one side the ability to request a retransmit, are there no error counters in the hardware for these digital entertainment protocols?
http://arstechnica.com/civis/viewtopic.php?f=6&t=275120&p=6271817
"If you think that the household mains looks anything like the nice sine wave we learned about in school, I suggest you go look."
Indeed. Been there done that. Some other interesting stuff in your post too (e.g. re current pulses/ringing from SMPS).
There is a whole load of junk talked on this subject to relieve gullible people of their money.But error correction is not a panacea, and having an error corrected digital link without commonly available tools to check whether it's working right or not is just stupid (or someone in the designer/manufacturers is hiding something).