What are positive and negative outcomes of requiring Ph.D. students to take a pedagogy course?
The main negative outcomes would probably be the opportunity cost - what else the PhD students could have been spending their time on - and the risk of developing a bias against such courses and the material contained therein if they are poorly designed or executed.

On the other hand, without critical reflection and exposure to alternatives, we tend to teach in the way we were taught, which may or may not be the most effective approach. Moreover, we may be unaware of common misconceptions and difficulties with our material, having either overcome these hurdles long ago or having sidestepped them. A good course can help with this, especially if it has a subject-specific component as opposed to being completely general.

Since you refer to a mathematics department, you might be specifically interested in Alcock &amp; Simpson's Ideas from Mathematics Education: An Introduction for Mathematicians.