Leela cuts down the Xmas palm tree. The next scene the palm tree is tied to the ship with a wrapped root ball, and is seen as a cut tree again while Amy is decorating it.
The Professor states that pine trees are now extinct, hence why they are cutting down a palm tree. But in the prior scene, there are pine trees shown on the mountain while they were skiing.
When Bender is heckling Conan O'Brien, Conan asks "Is everyone afraid of Y2K?" to which Bender replies "No, that was fixed 900 years ago." But this episode takes place in the year 3000, therefore Y2K was fixed 1000 years ago.