A teapot can last a lifetime and provide an invaluable service to your tea session. As a result it is well worth your time and effort to seek out and obtain a good teapot. The most important criteria of a good teapot is the quality of the clay. Good clay can smooth over and minimize the roughness in the character of tea, maintain a consistent temperature to effectively steep your tea leaves and thus provide a superior brew for our drinking pleasure and enjoyment.
A simple test to ensure that your teapot is made with decent to good quality clay is the hot water test. Start by pouring hot boiling water into your teapot and close the lid for 5 seconds before emptying out. Within this short time the hot water will have seeped into the small pores within the teapot and extracted some of the minerals and substances in the clay. Breathe in the rising steam from the teapot and you will be able to make a general appraisal of the quality of the clay. Strong odors that reek of mud, concrete, chemicals and other strange odors mean that the clay is of poor quality. A teapot made from clay that consist of these foul impurities will taint the tea that is steeped making for both an unpleasant and possibly dangerous brew (due to the leaching out of chemicals).
Additional Note: An old unused teapot that has been sitting pretty for many years may have very dry clay that is prone to crack under sudden changes in temperature. For such a case it is wise to soak the teapot in cold and warm water for a few days as a precaution before pouring in hot water.