What's the best way to evaluate students?

I went to see a professor today about an exam he gave us recently. I pointed out that often, when we have two professors writing questions for two sections of the same exam, the scores between the two sections have almost no correlation. He said that he had actually measured this in the past and found the correlation to be between 0 and 0.2.

And this is for graduate-level coursework, with essay-style exams written and graded by experts in their fields, and taken by pretty clever students, if I may say so.

My professor pointed out that multiple-choice tests are even worse, and in fact people tend to walk away from these tests knowing less than they did going in.

So how to solve this problem? Should we do away with testing altogether? If so, how can we differentiate students who learned the material from those who didn’t?