The audio engineer. Few pay attention to them -- unless something goes wrong. Much like many other below-the-line jobs, a quality mix is simply an expected occurrence. Everything should sound great. Why wouldn't it?
While audio engineers are often spared from the glare of showbiz, the job itself still has its challenges. Among the most difficult: clear wireless audio transmission & monitor mixes. Things have gotten easier in recent years as more advanced digital transmitters have become available. Performers can, with a relatively small investment, be all-wireless: mic, guitar pickup & in-ear monitor. The advent of in-ear monitor mixes is most significant, as feedback is most likely to occur via traditional on-stage monitor systems.
Recently, I have been focusing on setting apart specific parts of the audible spectrum for specific instruments. Just as wireless transmitters should be configured to reduce possibility of cross-talk, instrument sounds being transmitted to the ear should not have to compete with another instrument en route.
The mixer, itself, is an instrument. Depending on the venue & intent of the producer(s), it may be used to transparently amplify, highlight specific instruments over others (e.g. brass vs harp), or alter incoming sound to produce an effect. It is the responsibility of the sound engineer to both create a decent set of mixes (house, monitors, remote broadcast, etc.) & also reflect the intent of the producer(s).