This is a review of a partial completion (17/26). I usually don't drop anime once I've finished so much of it, but I did in this case, and will try to detail why below.
First of all, I confess to having a certain bias against the aesthetic of Last Exile. It's an older anime, and it feels even older than it is when watching it. I'm also not a huge fan of steampunk. But while that may have influenced my personal enjoyment, I try not to let it affect anything else (for the record, the "Enjoyment" category got a 3/10).
I'll run through each of the review categories.
I gave the story a 3/10. This is because, honestly, I never felt I had any idea what was going on. So, our two main protagonists end up on an adventure and get involved in world-altering events. That's a pretty standard story. But that's neither good nor bad. What makes a story great is when there are clear and compelling bases behind not just the characters' actions, but behind the world. While the characters get a little bit of clear but not compelling support, the world gets next to nothing. I felt like I understood what was going on with at least Claus, Lavie, and perhaps Alex, but I was blank as to what was going on in the world. Locations feel similarly drawn out of thin air. Of the various locations we are taken to, none of them feel developed. And some of them simply aren't; I don't even know what the Grand Stream is by episode 17. That's an issue.
I gave the art a 7/10. I'm honestly not one to criticize art that much anyways. It has an old aesthetic. I don't think that aesthetic can really be judged. If poor art actually starts to affect my ability to comprehend what's going on, then I'll rate it lower (for example, the anime movie Hells has a very interesting art style, but it actually has a negative effect on being able to tell what's going on). Last Exile does not have this issue.
I gave the sound a 5/10. I didn't feel anything from the soundtrack. The music is appropriate for the scenes, as are the sound effects, but they don't really enhance it in any way either. Similar to art, however, sound is a very subjective category that is hard to rate.
I gave the characters a 4/10. As mentioned when I was covering story, the characters get some clear, but not compelling bases for their actions. Or at least, the major characters do. However, I felt the antagonists were one of the weakest aspects of the show, and were in large part the reason I felt compelled to stop watching. I have little patience these days for antagonists that speak or act in a meme-worthy "evil" manner. The best antagonists are the ones whose actions are justifiable from a certain perspective. Characters need to be believable. Even if we assume that such ridiculous antagonists are simply extreme narcissists, it still doesn't feel real without giving them counterbalancing traits that real narcissists have. Narcissism alone can't make a believable person.
Besides the poor character development, I also feel the need to mention the appalling state of the female cast. I don't intend to make this a feminist review, but I do feel that the way that Last Exile handles female characters is an issue. The show has an old aesthetic. Lots of shows may use an old aesthetic and therefore portray female characters in an older, more conservative sense. I don't think there's anything wrong with that. Nor, for that matter, do I necessarily take issue with ecchi or harem shows that objectify women. Those shows are designed to cater to a particular audience, and generally don't feel like they're validating a view. They're made to be entertainment, not to explicitly validate what they are showing. Last Exile, on the other hand, gave off the impression that it was, because it felt like it was an honest portrayal of how the creators felt. The world of Last Exile isn't a historical period recreation. It's certainly not an ecchi or harem. It does have a somewhat historical feel from the steampunk aesthetic, but it doesn't authentically recreate 19th century society, and several female characters are placed in strong, commanding positions, with matching personalities to boot. Despite this, these characters are consistently portrayed as emotionally weak, having breakdowns from which they must be rescued by associated male characters. The male characters, meanwhile, never have breakdowns of their own. In this way, the anime gives off a rather sexist impression. In any case, if that kind of thing bothers you in anime, I strongly recommend not watching Last Exile.
Overall, I give Last Exile a 4/10. It has a world that I really did feel inspired by at first. I really wanted to get to know this world and the characters in it, and discover what fates awaited them. Unfortunately, Studio Gonzo fails to deliver a strong basis for these things, and the imaginative world they came up with drops like a Vanship with low Claudia pressure.