A Night of Fright is No Delight - S1-E16
Continuity mistake: When Fred is reading his book in bed, he is wearing his pyjamas, but when Fred says "You got to be kidding", he is wearing his regular clothes, and when he, Scooby and Shaggy go back into the bathroom to inspect the bathtub, Fred is back in his pyjamas again.
A Night of Fright is No Delight - S1-E16
Continuity mistake: When Shaggy takes out his sandwich, the goldfish bowl next to him is empty. When he grabs the box of fish food, the bowl now has water and a goldfish in it.
Chosen answer: A ghost wouldn't have to keep any food in the fridge - they don't need to eat. So it is one thing that proves the ghost is not a ghost.