All Men Are Perverts: When asked for a prognosis, Dr. Mr. Horse asks his nurse whether she'd like it in the front or back.
Mr Seahorse: Stimpy being a male cat and all. Subverted in that he's actually constipated.
Mistaken for Pregnant: Stimpy was assumed to be pregnant, but it turns out that he was constipated the whole time. But Dr. Mr. Horse decides not to tell him and Ren the truth, so they never find out about it.
"Shaggy Dog" Story: Besides being a parody of dramas, the episode is one big buildup to the punchline that Stimpy is just constipated, not pregnant.