In the first segment of the first Anthology of Interest, the one where Bender is giant, Leela works at Planet Express. But Fry never met Bender by the suicide booth, and he clearly just accepted being a pizza delivery boy, so he would never have met the professor or started working at Planet Express... and Leela would still work at Applied Cryogenics.
Also, in the third segment, how can the crew (excluding Fry) know each other? Amy, the Professor and Hermes would still know each other. But if it wasn't for Fry, Bender would be dead and Leela still work at Applied Cryogenics. I know, they're just fantasy episodes. But still...