I'll start things off with a warning: Don't watch Nadia: The Motion Picture if you haven't seen the original anime first. Viewing the original series first is a prerequisite to understanding and following the references in the film, as nothing is explained further for you and if you haven't seen the series, you will be bombarded with a lot of fragmented previous storylines that make no sense in the film's plot.
This movie does a lot of recapping the series utilizing the plot device of having Nadia remember the past, but just as human memory is unreliable, so are Nadia's memories. Her "recollections" are scenes taken from the original anime, but backstory elements have not been removed, and there are a lot of references to things depicted back then that do not make sense at all in the separate context of the movie. So, although her "memories" are sequential, they don't make sense as haphazard scenes showing random events are on display.
The story of the movie, like that of the original anime, involves the takeover of the world by an insane, power hungry megalomaniac named Geiger. Like his original anime predecessor, Gargoyle, Geiger believes humanity to be ultimately worthless, and doesn't mind expending as many human lives as necessary to achieve his goal of world dominion, but unlike Gargoyle, he doesn't have a grand motivation behind his actions. At least Gargoyle had a goal: the resurrection of the glory of Atlantis, by creating a Neo-Atlantis. Geiger doesn't EVEN have a reason -- he just wants to take over the world.
Somehow, Geiger has access to some Atlantean technology and knowledge - he recognizes Nadia as the former princess, and his naval vessels bear strong resemblances to the Garfish. Geiger also has a genius scientist creating sentient robots for him, which he is using to replace world leaders. Under his guidance, the robot replacements are working to start a new world war, after which Geiger can step in to rule what remains.
Nadia, working as a reporter in London, gets wind of Geiger's plan and meets up with Jean in France, who has unwittingly rescued robot scientist's daughter, Fuzzy. Together again, Jean and Nadia team up to stop the evil robots, prevent a world war, and defeat the evil Geiger. Comic relief is added when the duo teams up with former partners Grandis, Hanson and Sanson, who have a new model Gratan to bring into play to counteract the enemy's technology.
The animation flows fluidly, with nice character designs and handsome backdrops, so animation quality is pretty decent, but the background is not as detailed as it was previously and it comes across as muddied and not as clear and rich as in the anime. Special effects are dated, and nothing special to be seen during explosions or battles.
Sound effects also seem dated, with missile blasts and weapon detonations sounding weak and distant. Computer and machine noises also seem rather cliche. The background music and sounds compliment the action on the screen but are not memorable nor outstanding in any way. They are there, period. Serviceable at best. Same with the OP and ED theme songs.
The characters receive almost no development: Nadia and Jean are presented as we last saw them, and end the movie much the same for their adventure as when they started. Similarly, Grandis, Hanson and Sanson reprise their former roles, burt they don't even get any backstory shown to add dimension to their characters here. New characters include villain Geiger, who is merely a puppet megalomaniac to lead the bad guys, and deluded, disillusioned scientist Dr. Whola as a Nemo substitute and father for Fuzzy, and Fuzzy herself, the robot daughter replacement who serves as the focus of Jean's attention when he isn't devoting himself to Nadia. Whola and Fuzzy get brief backstory mentions, while Geiger gets nothing. They exist to fulfil their roles in the current story and that is all. Only the small amount of history given to Fuzzy is meant to garner audience sympathy, and it is too little for us to care what happens to her, nor to feel anything during her melodramatic final moments on the screen.
In short, there is nothing here to enrich the story obtained from watching the anime, nor anything new presented to add to our enjoyment of the franchise. It's just another adventure for Jean and Nadia, and not a very thrilling or suspenseful one at that.