The questionable penis-shaped tin in the kitchen is actually a lobster.
Sophia's lack of tact is sometimes explained by Dorothy after the fact as the stroke Sophia had in the past which caused her to be placed in Shady Pines (though this is rarely referred to otherwise). The stroke and her propensity to say rude things was only fully described on the first episode.
Corpsing: The reaction in the episode where Blanche gives the other girls calendars with erotic pictures. Apparently there really were some nude shots in there.
Shout-Out: When Dorothy is working on the kids' show, Mr.Terrific has a puppet sidekick named Kolack from Twilar. This is very likely a shout-out to Danny Thomas, who appeared on a The Dick Van Dyke Show episode ('It May Look Like a Walnut') as "Kolack from Twilo." Tony Thomas, one third of the production team, was Danny Thomas' son.
The episode with the live chicken, Count Bessie, had to be rewritten slightly in regards to who was standing where during the scene, because Bea Arthur, despite being known as an animal lover, had a phobia about live chickens.