Arc Fatigue: The entire "Upsidaisium" story arc is only 36 segments long in 18 episodes. And if you think that's bad enough, you should know that the very first story arc of the show, "Jet Fuel Formula", is only 40 (count 'em: 40!) segments long! All in an arc spanning 20 episodes!
Also, one of the parts of "Metal-Munching Mice" is "Fright Flight, or A Rocky to the Moon".
Nightmare Fuel: Gidney and Cloyd's first appearance in the pilot episode was a bit spooky, with the two fading in and out Cheshire Cat-style with creepy early '60s "spacey" sound effects. The limited animation actually made the scene eerier.
Boris looked pretty menacing in his first few appearances.
The Metal-Munching Moon Mice.
Also in the Pottsylvania Creeper story is the Pottsylvania Creeper, a plant that eats everything in sight, including people. Then its vines form a rocket that explodes in the air, which produces more Pottsylvania Creeper seeds. At the end of the story, we never again see the people it ate. Since Boris, Natasha and Fearless Leader also get eaten at the end, this should be Fridge Logic since they show up alive and well in future stories.
The Problem with Licensed Games: Rocky and Bullwinkle got three unique games on the NES, SNES, and Gameboy respectively, and all three were unplayable disasters.
Values Dissonance: There was some racial stereotyping in the Peabody and Sherman sequences involving Chinese and Native Americans that wouldn't be allowed today. Fortunately, the recent movie avoided this completely.
Viewer Gender Confusion: June Foray's voice for Rocky is an all-time classic performance, but it sounds distinctively female despite the cartoon's insistence that Rocky is male.