At the end, the arm of the statue of liberty falls off. The arm has the torch. In "Space Pilot 3000", the statue isn't holding the torch, but a transport tube.
At the beginning, it is stated that New New Yorkers elected a super-villain governor who stole the world's monuments, although the statue of liberty is seen where it belongs at the end of the episode.
It would take another 1000 years for the Omicronians to reach Earth. Unless Omicronian spacecrafts travel 1000 times faster than light.
Omictonians seem unaware of the concept of reruns. If they had been patient and waited, the finale of the show would have eventually been broadcast on their TVs.
When the attack started at the beach, the sky turned orange. But when a little spaceship destroyed Fry’s sand-castle, the sky was normal blue but in the next scene it turned orange again.