What are disadvantages of progesterone only pills?

Irregular bleeding. The main drawback is that estrogen-free methods are associated with more breakthrough bleeding or irregular bleeding.
No estrogen. #1 slightly higher risk of unintended pregnancy. #2 less effective "cycle control" as compared to "regular" or combination ( progestin and estrogen) birth controp pills. On the positive side, they can be used while nursing or other times when estrogen is inappropriate.