Leela uses a laser hatchet to cut the tree down, but atop the planet Express Ship the tree has its roots, wrapped in a burlap bag.
Everything that Bender and the other robots stole from that lady suddenly disappears in the next shot when they see Fry and Leela getting attacked.
Amy Wong and her family are extremely wealthy, but she shaved her hair off to buy Hermes a pair of hair combs. But then again, Bender has been emptying Amy of her money several times, such as in The Series Has Landed where he poured all the money in her wallet into himself.
Hermes shaved his hair to buy a set of combs for Zoidberg, however he clearly has hair after he has finished playing the piano in the final scene.
The Professer states that pine trees are extinct, however they (or at least similar trees) were present on the ski slopes, however these may have been artificial.