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.
Broken Base: The Adored by the Network status that this show held on [adult swim] and continues to hold on Toonami. Even fans of the show agree that it's been rerun to death ever since it first premiered, and just when it seems like the show will be given a break, the production crew behind Toonami still insists on bringing it back and airing it. That being said, there are still those that contest that Toonami isn't complete without Cowboy Bebop.
Complete Monster: Vicious. The reasonable response to your best friend seeing your girlfriend is not to sadistically force her to decide between her own death and having to kill her lover herself. Vicious has loyalty to nobody and thinks nothing of betraying former comrades to death or prison... he doesn't even register when men loyal to him give their lives as they're expendable to him. He also has no qualms about betraying anyone, whether he's usurping power from his leaders or cutting the throat of the foster father who saved his life.
What's frightening about Vicious is that it's hinted that he wasn't always a nihilistic psychopath. Flashbacks showing him with Julia and Spike show him actually looking happy, and there are many hints dropped along the way that the three of them were True Companions. Finding out that the two people he was closest to were planning to betray him seems to have pushed him over the edge. While Vicious has probably never been a "good" person, the fallout over Spike leaving the Syndicate seems to have made him worse. His nihilism and comfort with death also suggest that like Spike, he's already a dead man walking to some extent.
In The Movie when all the classic war planes are taking off one of the planes is piloted by the three old guys. As they're taking off one of them asks the others where they're going and gets the (incorrect) response that they're "going to sink the Bismarck". The plane they are flying in is the same model of plane that delivered the crippling torpedo shot to the Bismarck. In a further bonus the name of that model of plane is Swordfish.
All the written Chinese (no, it's not Japanese, despite the origin of the show) and other languages.
The chess game between Ed and the Chessmaster.
Germans Love David Hasselhoff: While it's still respected in Japan, this series is one of the most beloved anime in Europe and especially America. This is partially because it uses so many American action-movie and Western tropes that at times it seems like it was made for a Western audience.
The episode "Wild Horses" has an old old Space Shuttle being brought out for one last mission. The shuttle? Columbia. Cartoon Network actually pulled this one off the air for a while after the Columbia was destroyed during re-entry. Even worse, the episode mentions the shuttle's heat-resistant tiles being damaged, which is what caused the real Columbia to be destroyed.
Cartoon Network also pulled "Cowboy Funk" from it's first run in September 2001 for its depiction of a pair of identical skyscrapers being destroyed by a terrorist.
As was "Waltz for Venus" for the opening scene of terrorists taking over a commercial airliner.
In "Jamming With Edward", Jet making fun of Faye's age provides some really depressing Foreshadowing.
The Movie didn't get an American release in theaters until two years later due to its terrorism theme and that the movie made its run in Japanese theaters just days before 9/11.
Hell Is That Noise: "Pierrot le Fou" has two. The first being the creepy cover of Pink Floyd's "On The Run" that plays during the scene where Tongpu is being experimented on, the second being Tongpu's deranged laughter.
Hilarious in Hindsight: Back in the early 2000s, some advertisements mistakenly stated that Cowboy Bebop was a part of Toonami, which was still airing on Cartoon Network at the time. Fast forward to 2012, when Toonami is revived and now airs during [adult swim] hours. Cowboy Bebop finally makes its debut on Toonami, albeit as a holdover from [adult swim] Action.
Gren admits to Faye that "women aren't [his] style," and much of his interaction with Vicious could be read as jilted former lovers. At the very least, it's very much in Vicious' character to be aware of Gren's affections and manipulating him through them.
Hype Backlash: It it one of the most highly acclaimed series in the west, and has a reputation for being enjoyed even by people who don't normally care for anime. Inevitably, some people will watch it and wonder what the big deal is.
I Am Not Shazam: Tongpu, the AcrofaticMonster Clown, is often mistakenly called "Pierrot", after his alias "Mad Pierrot" and the episode's title "Pierrot le Fou", which literally means "Pierrot the Madman".
He must have been popular with someone important, since he has a blink-and-you'll-miss-it cameo in The Movie in his "Musashi" getup.
Seinfeld Is Unfunny: While this series is still among the pantheon of Anime Classics, some minor aspects are not perceived as innovative as they once were.
The Superlative Dubbing by the producers of the English Language version is something this series has been praised for. However, given that the quality of dubbing in Anime has (generally) improved since 2000, though some people may disagree, this is a less than top selling point nowadays.
The group behind the Bebop dub went on to localize Wolfs Rain and Ghost in the Shell: Stand Alone Complex, both of which are arguably better than Bebop on a pure technical level. Yet it's the early work that gets more praise (not that GITS:SAC necessarily lacks it).
The Character of Spike Spiegel, while still one of the indisputably popular characters of anime and possibly in all medium in general for his badassery and cool attitude, ends up coming across like a clone of many other countless other generic cool guys that are found in more recent works of fiction.
One of the most well-known examples. In fact, the series is very often used as THE example of what an English dub can/should be.
For original-language purists in the Anglosphere, it's often the ONLY exception to their Japanese-only rule.
The Mexican Spanish dub is not a slouch in this department either, despite having some not-too-serious translation mistakes.
Cowboy Bebop is one of the most consistently well dubbed animes of all time. Other famous good dubs of this anime are, among others, the Western European languages: European Spanish, French, German and Italian.
Too Good to Last: Shooting Star, the first manga spinoff. It was meant to run for a year but got cancelled after just ten instalments. Due to its being made while the anime was still airing, it had an almost completely different continuity, which may have been the deciding blow against it. Yet, many reviewers in the West considered Shooting Star superior to the second manga spinoff (this one simply named after, and hewing much closer to, the show) due to its lively artwork and interesting, though abortive, story arc.