For an example possibly familiar in computing circles, Infiniband has easily-accessible counters to record transmission errors. In a properly-built system with hundreds of communication-busy nodes connected with copper, you see remarkably low error rates, even in comparison with the spec (maybe a few a week in my experience).
Infiniband is using extremely isolated and well balanced cables for passive/copper transmission. Also the cable lengths are very short for EDR and beyond (3m-5m is max usable length). For anything longer you need to use fiber cables with embedded converters.
We have a cluster with ~1000 nodes and all generations of Infiniband (DDR/QDR/EDR) equipment, and routing all these copper cables without damaging them is not easy.
The quality of digital tranmsission over copper cables is dependent on the size and clarity of "eye", which is the pattern which two sinusodial signals when run through and oscilloscope. Lower quality cables (HDMI/DP/Coax/etc.) has blurry and small eyes, which increases chances of artifacts and drives the error correction modules harder, while better cables are easier on the both sender and receiver, since they produce lower number of errors to correct.
Trivia: Amphenol / Gore has high speed digital interconnect cables called Eye Opener Plus [0], which also used some of the Infiniband cables that we use.
