When Mr Peanutbutter calls Princess Carolyn, she is doing yoga and is in the middle of cat pose.
The orca whales at Whale World all have a dorsal fin collapsed to one side. Dorsal fin collapse is an abnormal condition common among orcas in captivity. Almost all wild killer whales have healthy upright dorsal fins.
The rabbit that BoJack and Diane follow at Goober's club, Whale World, is an "Alice in Wonderland" reference.