I was a CD early adopter (oh the shame!) and have a number of first issue CD's from 1983. None show any signs of deterioration and play just fine today (boy has CD sound come a long way!).
I also have a number of laserdiscs, and a number of these do show signs of laser rot, which as Sugarbrie notes appears as colored snow in the picture.
On laserdiscs the picture is analog composite video while the audio appears in both analog and also in digital form (on most laser discs). Thus picture quality directly correlates with the disc condition.
CD's are different, though. The digital data includes powerful error correcting codes in addition to the raw music data. This ECC code, which includes redundant data, allows the player to recognize almost all damaged data reads and to perfectly correct most of them. If the player cannot restore missing data bits from the ECC code, it attempts to interpolate the missing data (error concealment). If the data gap is too great for this, the player mutes.
Note that error correcting codes are also used to keep your internet traffic error free.
To increase the probability or error correction, CD data is not recorded linearly bit-for-bit along the pit tracks (i.e., not like music in a record groove). Instead data is written discontiguously in small blocks specially encoded to make the player's reading job easier. The player maps these "symbols" back into data words, then reorders the discontiguous data stream into the original 44.1 khz bit stream (for each channel!).
This discontiguous recording means that local disc damage will affect small data blocks from separate parts of the original data stream. Such damage is usually easily corrected by the ECC codes and unlikely to result in error concealment.
Sony/Phillips assumed that all discs would contain manufacturing imperfections, dust and minor surface damage. Thus a CD's sound does not degrade in proportion to disc damage or flaws.
Up to a certain point deterioration produces no effect on the CD's sound. After that only certain portions of the disc with especially heavy damage would show ticks or pops as error concealment takes effect. At worst case the disc would skip in spots or stop playing.
I'm not sure how Sugarbrie gets the increasing noise levels on old CD's.