When Zoidberg emerges from the escape pod in the flashback, his body resembles his current, more larger shape, in the next shot, he is seen in his younger, slimmer shape.
When Zoidberg takes off his helmet to eat the food in the first planet express ship, he should have died due to the rip in the hull seen in the background. When Zoidberg finishes eating, the hull is repaired.
When Zoidberg finishes gobbling the food, he has several large ketchup stains on his suit, but seconds later they have disappeared.
Zoidberg's helmet reappears on his head in time for the crew to escape the first Planet Express ship before the space whale eats it.
When the crew is accelerated to the back of the bridge after harpooning the whale, Bender is both the first and last to hit the wall. He is followed by Amy, Fry, Hermes, Zoidberg, Leela, and then Bender again. Bender appears twice and the first Bender's fingers can be seen in the final frame, when the "second" Bender's body is fully visible on the top of the stack.
In the fourth dimension, Fry's pupils are miscolored for a frame.
Leela is only wearing her space helmet, not the whole suit, when the whale bites open the ship - so she should be killed by the vacuum; additionally, her helmet and jacket both disappear when we see her "in the belly of the beast".
When Professor Farnsworth is cutting Zoidberg's hair, the razor moves Zoidberg's scalp shell as if it was skin. Zoidberg is hard plated at the time and had his skull almost crushed in "The Silence of the Clamps" and "The Tip of the Zoidberg". Zoidberg could only have his skin move by an object if he molted but since he had hair on, it was impossible for him to molt with it intact.
When they pick up the statue, when not zoomed in on the text all the "N's" can be seen as "K"