The elements Bender claims to be constructed out of change throughout the series (though given Bender's nature, it's possible he's lying). This became an in-joke amongst the writers in later episodes.
In Season 4 Episode 12 "Where No Fan Has Gone Before" Fry mentions the Star Trek films attracts negative attention because the show was banned long before then, and apparently saying the show's name is forbidden. In Season 3 Episode 8 "That's Lobstertainment!" at an Oscar awards ceremony a featured film is titled "Star Trek: The Pepsi Generation" and no mention of Star Trek being forbidden is made.
In many episodes the Earth's knowledge of things that have happened in the past is lacking, due to an apparent loss of historical documents throughout time (for example, in Season 1 Episode 2 "The Series Has Landed" it is made clear humans don't know the exact details of the first moon landing, or in Season 5 Episode 2 "Jurassic Bark" it is unclear how a 20th century pizzeria operated,) yet many people from Fry's time period are still alive, such as Richard Nixon or Leonard Nimoy's head. Also, even though characters do not know the details of important events in or before the 20th century, many characters make references to popular songs of the past (William Shatner in Season 4 Episode 12 "Where No Fan Has Gone Before", Kif in Season 3 Episode 5 "Amazon Women In The Mood".)
In several episodes the heads in the jars are fed (Spock is fed with what looks like Goldfish food) but they have no way of digesting this.
Leela's biological father is a mutant; one of his traits is that when he speaks his mouth appears to run vertically and open horizontally, whereas it is the opposite for a "normal" person. The problem with this is that he goes back to having a normal, human-looking mouth when not speaking.
Fry is frozen in New York; 1000 years later he is unfrozen above ground despite old New York being built over.
Some of the heads (in jars) are not anchored down, generally these should float.