A Tissot Indicatrix is useful method for communicating at a glance the kinds of distortion a given projection is prone to (in the figure below, each of the red circles occupies the same area). I've been told that popular methods for generating TI's have their own problems, to the of being sometimes woefully inaccurate.

What is the problem with the popular methods, and what is most correct way of generating a TI that is accessible to your average GIS dude(ette)?