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)
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)