Awesome Music: The main theme. WHOAAA! GATCHAMAAAAAAN! GATCHAMAAAAAAAAAAAAAAAAAN!
Lets Fly from the OVA. LETS FLYYY!!!!
Broken Base: Most notably in the terms of the English adaptations. Did Battle of the Planets have its own merit, or was it an unforgivable hack job? Is G-Force more faithful of an adaptation or did it do worse damage to Gatchaman's reputation? Even the uncut ADV dub is debated over, due to some corny added jokes and slang inserted into the scripts, some mistranslations (changing "Utoland" to "Jutland"), as well as some line changes that came off unnecessary (ie: Ken's scream of "JUN!" at the end of an episode was changed to him yelling "GALACTOR!").
Remakes such as the OVA, the live action film, and "Gatchaman Crowds" are subject to much scrutiny and debate over their flaws and merits, due to how much liberties they take with the original source material. In the case of the last one, the production doing away entirely with the "birdstyle" suits and containing no familiar characters but Katse already earned it a very negative reception before its airdate.
Berg Katse's rewritten origins in both the live-action film and Crowds have caused some base breakage. In Crowds, the renamed "Berg-Katze" is a former Gatchaman who's an alien and has destroyed planets, and has his own super-powered form. In the live action film, Katse's real identity is that of Naomi, a young woman who was a potential recruit for the Science Ninja Team and Joe's fiancee (who Ken also had unrequited feelings for), but who was supposedly killed by Galactor. She managed to survive and become part of Galactor.
Harsher in Hindsight: The episode Farewell, Red Impulse. The title character gives up his life to save the world, including his son who just learned his father isn't dead as he believed for several years. It makes the episodes he appears in earlier in the series much more painful, especially the occasional rivalry between G-1 the son and Red Impulse.note In Japanese culture, Kentarou "Red Impulse" Washio leaving his son Ken behind as a child to secure his future, by securing the world's future, is one of the most selfless and loving things he could have done, considering the Japanese stance on family and its importance to society; here in the West, however, he's viewed as a neglectful or even abusive father who left his child behind to throw himself into his mission for years, and then dies when he's about to come back.
Narm: Episode 20 ("A Critical Moment for the Science Ninja Team") is infamously known in the fandom as "the puppy episode" and considered laughably bad, for the plot of Joe winding up with shrapnel in his head (after saving a puppy), which Dr. Nambu tries to remove- via spinning Joe around in a centrifuge.
Joe's obsession with the cyborg girl Kathy in Gatchaman II is also regarded as rather silly, considering that he only knew her for about a day yet displayed an incredibly melodramatic reaction to her death that he hadn't previously shown for anyone else.
Sequelitis: The two follow up series, Gatchaman II and Gatchaman Fighter are generally regarded as inferior to the original for various reasons.
Values Dissonance: Kentaro Washio is seen as a callous, cold and selfish father who abandons his son Ken aka G-1 to work as Red Impulse for the peace in the whole world. In Japan, however, he's seen as an heroic figure who loves his son so deeply that he sacrificed their time together to to protect the world so Ken will have a future.
Ken punching a young girl in the stomach in an early episode did not earn him too many favors in Western fandom. Neither did him slapping the same girl later in the episode, or him slapping Jun in episode 40 (to be fair here he was reprimanding her for running off on her own and almost getting killed and making the rest of the team worry). These can definitely be chalked up to different standards of the era and culture, though it can still be jarring to see.
Jun being slapped by Joe in another episode tends to get more cringe reactions, along with another slap moment from Ken in "Gatchaman II". In moments that aren't related to her being slapped, her fright over a robotic ant in an early episode or other moments where she comes off less strong or relying on Ken for advice tend to be critiqued (see "What Measure Is A Non Badass" below). The "Battle of the Planets" and "G-Force" adaptations attempted to vindicate her by either cutting these moments of panic or changing her lines to make her sound more knowledgeable or tougher.
What Measure Is a Non-Badass?: Many people think Jun is just a useless Chick and not as "strong" as modern heroines. Thing is, considering that the series was written in The '70s, Jun's character was actually revolutionary by that time's standards, kicking ass with the best and blowing up stuff real good as the team's demolitions expert. She and other girls like Francoise/003 and Sayaka Yumi were among the first Action Girls of oldschool anime, setting the precedent for many other more action-oriented ladies in anime/manga as a whole. Not to mention her all-male True Companions treated her with respect and care (with the exception of Jinpei, and he still didn't go that far) and they stuck by her side whenever she needed it.
Woolseyism: Some episodes of ADV's dub venture into this, if not even outright Gag Dub. "Murder Music" (41) is a memorable example, although there are just as many fans that hated its dialogue changes. The dub of the episode changes the Demon 5's song to a number called "Battle of the Planets", providing shout-out to the first English adaptation.
Some changes in dialogue for ADV's scripts were also used to correct minor continuity errors in the original note such as Joe being publicly referred to as "Condor Joe" when his identity is supposed to be secret at that point (episode 27), although there were other points where mistakes and mistranslation were made, or (see Broken Base) deemed unnecessary changes.