When Haney is attempting to sell Mr. Douglas a cake for Arnold with a message on it he sets each one down but when she brings another one out the previous cake is gone.
When Lisa adds chocolate syrup to Oliver's 'hots cakes' birthday cake and turns her back he takes a big bite out of the candle. There is some chocolate syrup clearly seen on the candle he has bitten a piece from but when Lisa turns back to him not only is the syrup now missing but the candle is longer too.
When Kimball drops by with his noise maker looking for the birthday party we see even though the entire room is lit up, the light switch by the door in the off position. This is the same switch that turns on all the lights in the dark room after Oliver returns from Ziffel's thinking there was a party over there.