Love 'Em and Leave 'Em - S1-E8
Continuity mistake: After Luigi says "Let's play cupid," he peeks around the corner along with Peach and Toad down at Mario going down the aisle with his "bride-to-be." Luigi, as expected, has been wearing green all episode, but when you see them peeking around the corner, Luigi's hat has become red. In the very next shot showing Luigi from behind, his hat has returned to green. (00:14:40)
What Price Gloria? - October 16, 1961 - S2-E4
Continuity mistake: When Sam goes out of the window to save Gloria, part of the ledge breaks off, but in the near shots it is broken off almost to the corner near Gloria, while in the shots from below most of the ledge is still intact. (00:35:45)
Chûgoku kara kita aitsu! Chotto hen!! - S1-E1
Other mistake: When Ranma is battling Genma at the very beginning, she slides into the main road. Behind her is a vending machine for drinks, only, it's marked "DOLINK" (bad transliteration). (00:03:00)