The goat portrait in BoJack's room mimics Vincent Van Gogh's "Self-Portrait" (1889). Presumably the painter's name in the BoJack Horseman universe is Vincent Van Goat.
This is the first episode to not have an opening credits sequence.
The rehab center is called Pastiche's. A pastiche is "an artistic work in a style that imitates that of another work, artist, or period." This may be a reference to the facades put on by the inhabitants of the center or a reference to real-life Malibu rehab center, Passages, among other possibilities. It also sounds like "Past issues."