These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Angst? What Angst?: Fry and Leela don't seem too bothered by the idea that everything in the universe is frozen in place besides them in the series finale.
Played for Laughs in the pilot, where Fry actually expresses joy for leaving his old time period, though a later episode suggests that he just convinced himself that his past was horrible because he knew he could never go back.
Better on DVD: The original run was broadcast out of order and at erratic intervals (to the point that there are actually five broadcast seasons made up of four production seasons). The DVDs and Netflix streaming allow you to watch the series as it was originally intended.
Broken Base: The made-for-DVD movies and the Comedy Central episodes. Either they're just as good as the FOX episodes or they're an inferior copy of the infinitely better FOX run. Ditto the first couple episodes, where the voice acting was kinda off (especially for Bender), everyone's characterizations weren't fully developed, and most people thought the show was So Okay, It's Average (or dismissed it as "The Simpsons in space").
Jack Johnson: It's time that someone had the courage to stand up and say: "I'm against those things that everybody hates!"
John Jackson: I respect my opponent. He's a good man. But frankly, I agree with everything he just said!
Cargo Ship: Scruffy owns a robotic Washbucket with a female voice. In one episode, Amy gets her brain switched with the Washbucket, and Washbucket declares her love for Scruffy. Scruffy declares his love back, but turns her down because she's a robot even in Amy's body. She leaves the room, and he curls up and cries.
Crosses the Line Twice: Fry's repeated deaths in "Meanwhile." At first it's gruesome and horrifying, but after the fourth or fifth time, it becomes gruesome and hilarious.
Robot Santa's entire existence is based solely on this trope.
Designated Villain: There's the parody example of the Ball aliens that Earth went to war with on "War is the H-Word." As it turns out, it was the Earthican forces that were the invaders, the Ball people were just harmless aliens that only wanted to bounce. When Fry realizes this, he's understandably confused.
"Pop a Poppler in your mouth/When you come to Fishy Joe's!/What they're made of is a mystery/Where they come from no one knows!/You can pick 'em, you can lick 'em/If you promise not to sue us/You can stick one up your nose!"
In I Dated A Robot we see a video about how humans dating robots will destroy the world. Then we get Proposition Infinity and discover robosexuals are both common and repressed. Bonus awkward for the original tape being a high school health class video approved by The Space Pope.
In the pilot episode, the line about the Stop & Drop Suicide booths being "Americans' favorite suicide booth since 2008" becomes a bit wince-worthy in light of 2008's economic meltdown and the invention of an actual suicide machine in the same year.
Fry's delighted reaction to realizing that everybody and everything he knew in the 20th century has gone (since he thought they didn't seem to like, care, or even respect him) seems much harsher when subsequent episodes such as "The Luck of the Fryrish", "Cold Warriors" and "Game of Tones" have shown that his family actually did love him and were worried about him when he went missing.
One of the stations in the New New York tubeway system is given as "J.F.K., Jr. Airport". After the real-life John F. Kennedy, Jr. died when his private plane crashed, the line was replaced with "Radio City Mutant Hall" (though the original line can still be heard on the full-episode animatic that appears on Futurama volume one DVD).
Fry's last line before he got cryogenically frozen was "Here's to another lousy millennium". Eerily prophetic considering that 2000 to 2010 had a lot of terrible things happen both in America and globally (a major terrorist attack on American soil, economic failure, and natural disasters).
In "The Lesser of Two Evils", the main characters visit a theme park modeled on 2000s New York. There's a brief scene where the stock market drops from about 11,000 to 7,200, similar numbers to the real-life 2008 crash. (Fortunately, it jumps right back up to 11,000, and all the stock brokers who jumped to their apparent deaths float back up into the building via jetpack). Considering that the scene was supposed to be a "distorted history" take on the crash that started the Great Depression, that makes this a sort of bizarre case of life imitating art imitating life.
The plot of "Calculon 2.0" (about Bender and Fry plotting to return Calculon to life so he can return to All My Circuits) has become this, as by the time it aired the show had been cancelled again.
Incidentally, that very episode contains the line: "This must be a hard time for those who confuse TV actors with real-life friends." The episode aired right around Cory Montieth's death (although the writers couldn't have possibly known about it), making it a shockingly relevant line at the time.
Genius Bonus: A lot of jokes, references, and continuity errors are more understandable if you know anything about college-level math and science.
The series has a number of particularly extreme examples in which complicated jokes (possibly made in a fictional language) are hidden in the background and can only be seen for a split-second, requiring a very devoted fan to pause and get the absolute most out of episodes.
In The Beast With A Billion Backs, Fry's polygamous girlfriend, Colleen, joins him when everyone goes to Heaven with Yivo. Colleen was voiced by Brittany Murphy [in what is now her last voiceover role, not counting her role as Luanne Platter on King of the Hill], who really did end up in Heaven (all too soon) in December 2009 (and was joined by her husband not too long after).
The unnamed couple's clear, plastic tarps with strategically-placed black tape from the first episode ("Space Pilot 3000"), the futuristic club clothes everyone wears at The Hip Joint on "Love Labor's Lost in Space" and Leela's costume on "Bend Her" can now be identified as styles associated with Lady Gaga, Nicki Minaj, or Ke$ha.
The Couch Gag from the final original series episode? "See you onsome other channel." Doubly hilarious, considering that Futurama went from being rerun on Cartoon Network to rerun (and revived) on Comedy Central, and triply hilarious now that Comedy Central canceled it and there's a lot of rumors that the show will once again be revived somewhere else.
In "Bend Her", when Bender asks Farnsworth to make a woman out of him, Farnsworth misunderstands and says they should "just remain friends". We later find out that he actually has had experience with Robosexual relationships in "Proposition: Infinity"
In "Lesser of Two Evils" in the Old New York theme park there's a marquee that says Star Wars 9: Yoda's Bar Mitzvah. Not only did Disney purchase Star Wars with plans to make a sequel trilogy (episodes VII, VIII, and IX) but it was announced in February 2013 that there would be a Spin-Off movie based on Yoda.
In "Overclockwise" Mom spies on Bender and Cubert using the X-Cube 360's camera. Two years later, Kinect 2 on the Xbox One was announced to be mandatory and still listening even when left on standby, making people paranoid that Microsoft was trying to spy on them.
Bender's line "Damn you, Obamacare!" after learning that Fry didn't die from a heart attack is funnier (or more cringeworthy), considering the glitches and failures behind it.
Moral Event Horizon: Zapp Brannigan is a grade-A Jerkass, putting himself above others and commanding suicide missions. However, some may argue that he crossed the line in The Beast With a Billion Backs. Kif dies as a result of trying to go against the Dimensional portal Yivo. After hiding in a shack with Amy and Leela, Zapp begins "reminiscing" about Kif. Zapp then SLEEPS WITH AMY. So, yeah, the jerk used a widow's husband's death.... to get laid.
If he didn't cross it then, Zapp definitely crossed it in "In Gadda Da Leela." Leela and Zapp crash on an unknown planet, alone and without supplies. Leela is trapped under a fallen tree, and delirious from lack of water, and the Earth has apparently been destroyed. Through the episode, Zapp appears to be helping Leela get better. Then we find out that the planet they crashed on is Earth, and Zapp has not only been using their current predicament for an Adam and Eve Plot-style seduction, but placed the hazards there so that he'd have a better shot at sleeping with Leela(again). The writers themselves seem to know that what Zapp did was unforgivable: they originally planned for Zapp to get off scott-free, but changed it to Leela punishing him in a rather fitting manner.
What an Idiot: Dan McMasters from Murder On the Planet Express. After terrifying the crew and making them overly paranoid of a potential shape-shifting monster, he then has the "bright" idea of trying to calm Fry and Bender down even though they're both now scared out of their minds, and he does so without bringing the rest of the still-alive Planet Express crew with him to prove that he's telling the truth. All things considered, he probably deserved what happened to him.