Clearing things up about mud(dler) carp.

The distinction between a "mirror" carp and a "common" carp is the same as the distinction between green and blue eyes in people.  Simply put, it's just some genetic variation, showing up as physical traits, that are passed down from parents to offspring. 

Typical healthy "common" carp have small, symmetrical scales covering the whole fish.

Typical Mirror Carp have distinct scales that are BOTH Large & Irregular.

Fully scaled "mirrors" exist, but a mirror's scales are often in patches, exposing lots of bare, leathery carp skin.  

To quote master Yoda, "There is another".  That is, another distinct variation of carp, the "Muddler".

Muddler Carp are distinguished by having patches of small irregular scales.  Throwing off the order and symmetry of a typical common carp scale pattern.

The Small & Irregular scales can appear in patches located in seemingly random spots of a fish, or can cover the whole fish.

The muddler scale pattern is unique to every fish, like a finger print.

 Common Carp: Small, even, and symmetrical scales.

Mirror Carp: Large, irregular, and often patchy scales.

Muddler Carp: Patches of small and irregular scales.

Leather Carp: No scales at all.

Hopefully this will give you some ammo in the war of fishing snobbery.