Tolfdir is an idiot, no doubt. But that by itself is nothing new. There are plenty of idiots running around Skyrim. The problem is that he has been placed in a position of responsibility in spite of his shortcomings. I feel that fault lies at the feet of a much greater idiot - Savos Aren. Makes you wonder if he scoured the countryside looking for the worst mages he could find to surround himself with 'yes' men (and women).
That whole college is a disaster waiting to happen. . .oh wait, it did. Well, at the very least, when Savos dies perhaps they could find a better suited candidate for Arch-Mage perhaps not from the current selection of teachers. . .oh wait, they did. My goodness, that candidate wouldn't even really have to know magic and they would probably be a better fit. . .oh wait, they are. Well at least someone (Psijics) realized the utter incompetence passing for instruction at that college and figured they could do better with someone who would spend approximately 5% of their time at the college.