The Cobb-Douglas production function is a formula used to measure how efficient inputs like labor and capital are in producing goods. However, there are three paradoxes with this formula. Firstly, the cost functions can be both convex and concave, which goes against economic theory. Secondly, when labor is combined with more capital, it becomes more productive, contradicting the Law of Diminishing Returns. Lastly, there are ever-increasing returns to labor's technical productivity, even when labor and capital remain constant.