Other mistake: In season one when Alex got divorced, Joey and Gina talked about how Gina got divorced from Michael's father while she was still in high school. In season two, we learn that Jimmy is Michael's father. Joey didn't even know that they were together, he certainly would have known if they were married.
Plot hole: In the episode where Joey tells Jimmy that Michael is his son and they cut of some of his hair to do a DNA test, Gina tells Michael that he is missing some hair on the back of his head. In the next shot the angle changes, we can now see the back of Michael's head, and he's not missing any hair.