As a multi instructor, I believe that there should also be a minimum number of instructional hours on singles before being able to teach multi.
I have seen one accident and heard of many which I suspect were down to lack of teaching experience.
It took me around 500hrs as a single AFI/QFI before I had seen most student gotcha's and then be able to predict when these were about to happen. At least in a C152 I was able to learn from my lack of experience without bending the trusty workhorse.
One instructor I know of gained his AFI on singles, did about 50hrs teaching, and then due to his reasonable amount of twin PIC time went and became a multi instructor. His aircraft bit him in the hands of the student. Causing surface contact!
Only with teaching experience does the instructor on multi's have enough forward thinking to monitor the student without having to hover the controls. However, from time to time I still get the odd fright!
As they say, flying is one BIG learning curve.