Animation Age Ghetto: The mindset of animated works only being for children is averted, obviously, given the film's gratuitous violence and nudity and resulting R rating. Unfortunately, it ended up falling into the opposite trope.
Hype Backlash: The film is a perennial Cult Classic, but popular opinion has been steadily turning against it in recent years. There is much more adult-oriented animation available today than there was in the 1980s, and now that Heavy Metal has finally received a video release and it's no longer immensely difficult to find, people end up disappointed with the writing and tone, and some are put off by the gratuitous gore & nudity. That said, most people still agree that the soundtrack kicks ass.
Genre-Busting: It's an animated sci-fi/fantasy/horror anthology movie. Whether you think it's good or bad, you have to admit there really isn't much else like it.
MST3K Mantra: Since there were so many problems with production, the movie relies on the mantra a lot to make up for the plot holes and lack of continuity.
What an Idiot!: Harry exchanges the Loc-Nar to a mob boss. The Loc-Nar is shown to melt one of the workers who discovered it and is now safely encased in a protective capsule. You'd Expect: The mob boss to leave it in its casing. Instead: He opens the case and picks up the Loc-Nar, which melts him.
The Woobie: The poor little girl in the bridge segments who watches her father be melted away into nothing before having to listen to the Loc-Nar share its history of destruction, all the while being told she will meet the same fate.