In my view, one of the fundamental requirements of any instructor is to be able to communicate CLEARLY, both in annunciation and meaning, especially in the air.
I used to get fed up with instructors, and still do sometimes on the biennual, who did not make it clear what they wanted you to do e.g. demonstrating a stall - what exactly do they want you to do?
My only instructing experience was as an ATC gliding instructor and, when you think we used to teach ab initio cadets to solo in 30 - 35 x 3 minute flights, you had to be a very good communicator. Generally, the ATC instructors were made to be very good at it by the Central Gliding School instructors.
Another fundamental is consistency. Sometimes it seems too much to expect any one instructor to be consistent. Expecting consistency between two, even from the same school, is usually too much.
Two of my neighbours are learning to fly at the moment, one fixed and one rotary, and I have been horrified by the poor quality and consistency of their instruction and the waste of money this has led to.