In Series 3, Frasier has a pet dog called Pavlov. In Series 9, Frasier talks about never having had a pet.
When Frasier and Lilith enter the bar prior to Frasier discovering the dead rat in her purse, there are two garbage cans outside the door. When he takes the purse out to dispose of the rat, there are still two cans. Moments later when they go out the door to go to the theater, there are three cans. When Carla opens the door, it's back down to two.