Better on DVD: Among other things, Discotek Media's DVD and Blu-Ray releases not only restore the opening sequence that was absent from the 2006 DVD, but includes both Streamline Pictures and Manga Entertainment's dubs, as well as a "family friendly" version of the latter dub, making it easier to compare them and decide which one you prefer.
Broken Base: Sort of. You're not going to find many Lupin fans (or anime fans in general) who dislike this film. However, Cagliostro's glaring difference in tone compared to other entries in the Lupin canon have some fans call it out as a disgrace to its source material… even if they embrace it for being all-round enjoyable. The dichotomy has been explained thus: "Cagliostro is a great movie, but it's a bad Lupin movie."
The Manga Entertainment/Animaze dub has its own example on the swearing and whether or not it hurts the film. While the dub is overall more faithful than the Streamline dub, the swearing is thought by many to have gone against Miyazaki's intentions with the film, while others don't mind. For the former group, the Discotek release includes a version of the dub that removes most of the swearing, though it's alongside the version with all the swearing intact, which should satisfy both groups.
Contested Sequel: Though not being much of a sequel (since Lupin III runs on zero continuity), Miyazaki explicitly sets this film toward the end of Lupin's career, meaning it takes place after Mamo. Even fans who like both movies prefer not to think about them at the same time.
Fridge Logic: Lupin has his Walther P-38 pistol melted into slag by lasers in one sequence. One can only wonder how the heat didn't cook off the ammunition in the magazine or fuse the metal into his hand.
Germans Love David Hasselhoff: The movie was a failure on its initial release in Japan for being too cartoony and not having Lupin's adult humor. By contrast, Americans loved it and it's more well-known and sold far better than "Red Jacket" or Mamo. Two things can explain why. First, very little Lupin had made it to the States by then, so Cagliostro was the largest release at the time – many American anime fans were introduced to Lupin with this film. The other reason is that Streamline and Manga marketed it as a Hayao Miyazaki film, so viewers go in expecting something Miyazaki-like (which they will get).
Magnificent Bastard: Lupin, even when made more heroic, is still a devious plotter, manipulating people by reason and emotion.
Misaimed Fandom: Princess Clarisse was not intended to be the Trope Codifier for moë. Miyazaki despises that trope. As a self-avowed feminist, he thinks the concept of moë is a terrible fetish that devalues girls.
Moe: Princess Clarisse is popular among fans, was featured in early fanworks and doujinshi, and sometimes even said to be the first "moë" character. However, see above…
Sequel Displacement: It's ironic given what people thought of it at the time, but as Miyazaki grew more and more famous, this film went on to more or less overshadow most, if not all other Lupin III works, Mamo included.
Signature Scene: Either the mountainside chase or the clock tower showdown.
Vindicated by History: When Miyazaki made this movie, he put his own spin on the Lupin character, toning him down from the raunchier, more manic version depicted in the manga and animated series (apart from the second half of "Green Jacket", which Miyazaki and Takahata directed). As a result, it flopped in Japan when it was first released – the people who liked Lupin for what it was were turned off, and the people who didn't like Lupin didn't have any reason to watch the movie since no one in 1979 had heard of Hayao Miyazaki. It was only years later, when Miyazaki gained recognition for his original works with Studio Ghibli, and more people watched the movie without any prior Lupin experience, that it belatedly gained a reputation as a classic. Other animators in both Japan and America liked it and would Shout-Out to it, which drew people in to discover what was being (often subtly) referenced.