This, the first and arguably greatest Harlock anime, is its own self-contained continuity. It does not, and could not, cross over with any subsequent Harlock anime series.
Space Pirate Captain Harlock was a product of its time, to be sure. The year 1984 had yet to arrive, and the Orwellian themes of Big Brother and dystopian societies looming just over the horizon found their way into the world structure of Space Pirate, as did the then-trendy (and now somewhat hokey) "ancient astronaut" theories about the pyramids being designed and built by aliens, how the Mayans invented television, and so forth. Matsumoto's own feelings about the Japanese government of the day also figured prominently in the story, with the mindlessness of political bureaucracy paraded about in a social satire bordering on-and sometimes stepping right over into-parody. The world of Space Pirate feels predominantly that it has "arrived," and consequently has settled into contentedness and lost its spirit. A small and derided few believe in man's future as a spacefaring species, and have begun the exploration of their new ocean, but most would rather let robots develop extraplanetary resources and ship them back to earth, freeing the human populace up to lounge about and watch crappy TV-much like most modern people would prefer if there were only enough robots.
It's important to note at this point that mankind has yet to encounter any alien civilizations in the course of its space explorations, resulting in the complete unwillingness by the earth's parliament to believe in the possibility of an extraterrestrial threat, or frankly, in extraterrestrials at all. Consequently, any attempts to place the narrative of this story subsequent to, but connected to, the events in My Youth in Arcadia falls flat, since Arcadia begins with the occupation of the earth by aliens. Even the most thickheaded of politicians wouldn't be likely to totally forget the events of a war occurring only seven or so years prior, with the possible exception of...most all of them. Heck, maybe it's not so implausible, after all.
Through flashbacks we learn that Harlock and his best pal Tochiro Oyama, who have been friends since kindergarten, have left this totally unhip and unhappening earth to seek their fortunes in space. In the course of their travels, they run across Emeralda, whom Tochiro falls for immediately. (Again, this conflicts with My Youth in Arcadia, wherein Harlock and Tochiro meet for the first time as adults, and it's Harlock and Emeraldas who seem to already be acquainted.) Through her, they fall in with refugees and anti-government fighters who are struggling against the earth parliament and the earth garrison forces, a bunch of really uncool cats who aren't above using slave labor instead of good old-fashioned robots if they really think you suck. Earth's Prime Minister wants Tochiro's mind in order to design new and more powerful ships and weapons (Harlock is barely worth their time at this point,) forcing the pirates to remain in hiding until Tochiro can complete the ship of his dreams. He and Emeralda have meanwhile seen the birth of their daughter Mayu, who is just starting to walk as the ship nears completion. With his anemia worsening, Tochiro nevertheless manages to finish the spacecraft just in time for the refugees to escape their hiding place on planet Heavy Meldar before it is torn apart by the approaching planet Ganda (a concept we'll see again in Queen Millennia.) He names the ship "Arcadia" in honor of a biplane flown by an ancient ancestor of Harlock's, which was named "My Youth in Arcadia," the craft in which one of a long-past generation of Harlock's family first sought the freedom of the skies. This also taunts the crap out of the viewer who is trying to make a timeline including this series and the My Youth in Arcadia film, which simply remains impossible.
Only minutes after the Arcadia's launch, Tochiro succumbs to his ailing health. His body is buried in space, and the grief-stricken Emeralda follows it as it drifts away. (We may presume that it was she who later took his body to earth, where we see his grave in the very first episode, but speculate is all we can do, as she never appears in the story again.) The Arcadia's central computer comes to life, and forever thereafter seems to embody the will of its creator (Harlock makes one passing reference to the computer containing Tochiro's brain cells, but how or when this occurred is never elaborated upon.) The computer as seen in Space Pirate is also bereft of speech (barring one crucial instance) and speaks to Harlock by making the ship creak and groan, much more in the tradition of a ghost story than of SF. In all other incarnations of animated Harlock, the computer speaks quite clearly with Tochiro's voice, and there is no ambiguity as to how he came to be embodied in the ship.
Until the Endless Odyssey mini-series was released, this was the only version of the story in which Tochiro and Emeralda(s) have a child, or even a particularly successful relationship (Mayu doesn't appear in the manga version, either, and her identity is never disclosed in Endless Odyssey; the filmmakers seemed to function under the assumption that their audience would know who she was without any exposition, which American importers Pioneer/Geneon rather embarrassingly did not). In most other stories, their travels take them in separate directions.
Harlock's crew all get their own backstories here, but while several of these characters will appear in subsequent anime (including Kei Yuki, Tadashi Daiba, and First Mate Yattaran,) they will invariably have different origins than the ones we see here. In Space Pirate, Kei is the daughter of Shuiichiro Yuki, an aeronautics engineer. When she reappears in Endless Road SSX, she's the daughter of Goro Yuki, a newspaper publisher (hey, it's not like anyone but teenaged computer geeks had thought of anything like the internet in 1982.) The only similarity is that both fathers die--fathers don't tend to live very long in Matsumoto stories, as a general rule.
While Space Pirate generally functions well as a self-contained storyline, even back then it seemed that Matsumoto couldn't resist throwing a few screaming monkeys with wrenches into the works: before the series had finished its run, a thirty-five minute featurette entitled The Mystery of the Arcadia was released theatrically. Basically an expanded version of episode thirteen, "Witch Castle in the Sea of Death," it nevertheless managed to contradict, rather than simply elaborate upon, the events of the original episode. Some dialogue is re-written, new observations are made by crew members, and new events (mainly Mayu spending a day aboard ship when all the other children at her school are visiting their parents) occasionally displace some old scenes, including that timeless classic of an instance of Harlock dropping in on a military base to use their telephone. Ah, yes...the dazzling, marvelous world of the future.
It's primarily the backstories and the attitudes of the earth government concerning alien civilizations that contribute to the isolated continuity of this series, but it's also worth noting that at the series finale, Harlock disbands the crew and, in the words of the narrator, "vanishes into the depths of space," taking only his, ahem, 'companion' Mimay with him. Therefore, any attempts to place other Harlock stories after the events in Space Pirate are going to fail just as surely as trying to place them earlier. The entire Harlock mythos is told here, from back to front, with all bases covered, all loose ends clipped, self-contained and fairly explanatory. When the public wanted more of their favorite pirate, there was nothing to do but retell it. And retell it, and retell it, and retell it. And eventually, as things tend to go, screw it all the hell up.