I worked in a CD foundry in the early 1990s. Scratches that were not tangential (perpendicular to the radius) were irrelevant, as the basic CD encoding scheme provide something like (IIRC) 30+ bytes of data parity protection. If the scratch width along the track wasn't longer than that, it didn't exist.

If it did exist, some toothpaste rubbed tangentially around the CD on your fingertips was often enough to buff it out, at least as far as the 30-byte limit cared.

It was a phenomenal jump in data integrity, built in at the recording level. Sure, you could encode even floppies with that scheme... but your computer didn't, natively.