I will attempt to make this mostly spoiler free, but I may end up leaving a couple hints about events in later episodes. The last paragraph in particular (starting with "finally", appropriately) will have some hints about the ending.
Essentially, Aldnoah.Zero is a science fiction anime focusing on ground combat. Simply watching various giant mecha, ships, and scenery get blown up in various ways is worth a bit of entertainment, as always, and this anime doesn't disappoint in that regard.
Mostly, though, I ended up thinking about the military and about war while I was watching it.
Part of that has to do with the massive technology imbalance. The Versian (hereafter "Martian", since Vers is just the name of the government formed by the colony on Mars) forces have technology literally generations ahead of the Earth forces. If I were drawing comparisons using modern technology, I would probably compare it to a modern armored cavalry unit attacking a trench line in WWI. On paper, there's absolutely no reason to believe the Earth forces should be able to pose any threat at all, let alone win.
Yet they do, and it's actually not horribly contrived, mostly because the Martian forces barely deserve to be called a military at all. The anime creates a picture of an almost feudal society based on the right to use their advanced technology, and the "knights" that that society produces hate working together, see each other as their primary competition, and trust far too much in their advanced technology... and they still inflict incredible casualties on the Earth forces in exchange for each knight the Earth mecha manage to take down. The Earth forces use good intelligence and quick thinking to find and exploit weaknesses in their enemies' advanced tech, but still have to take extreme risks to win and still have to retreat often when their enemies' weaknesses aren't known or can't be exploited. It seems rather realistic to me, inasmuch as that term can be applied at all to soft science fiction.
Which isn't to say I don't have problems... the most serious of which is that the Martian forces shouldn't need to come to Earth's surface at all in order to eliminate strong points. They're clearly capable of bombarding the surface from orbit, Earth just as clearly doesn't have any good weapons to take out orbital targets, yet the Martians never seem to notice or use that advantage at all. Given all the stupid things the Martian forces do in the course of this anime, though, that one is rather easily ignored.
As for some of the other details... well, I can't decide if it's a problem or simply an unwelcome reflection on the ability of military organizations to react quickly. The Earth forces, for all that they are much better organized than the Martians, don't seem to have the faintest clue what the Martians are capable of or how they should fight at the beginning of the anime. A lot of the redshirts that make up those incredible casualties I talked about simply charge into battle, guns blazing, trusting that AP bullets and HE grenades will work against gravity manipulation, plasma weapons, and advanced sensors and jamming capabilities. The good intelligence the Earth forces manage to get all too often comes at the cost of those lives... and I can't quite decide whether the anime is painting an overly negative picture of a military's ability to adapt to a previously unknown threat, or exactly the right picture.
For that matter, many of the pilots continue to charge ahead, even after they've had the chance to realize what the Martians were capable of. Some of it can be attributed to trust that the veterans among them will be able to figure out the enemy's weakness quickly, but some of it is just as pointless as it was the last time they tried it. I suppose that is the nature of the risk they're taking in order to win, even if I'd like to think that they should be trying for better intelligence.
I will take a moment here to note one more flaw - apparently the main character, a high school student, is a better pilot than almost all of the trained military pilots in this entire anime. Granted their alternate history has military training in high school after the first Martian war, so he's not completely untrained, and granted that his trainer has less armor and is theoretically more maneuverable than the actual combat model, but still, that's a little jarring. That he can also apparently think quicker and more creatively than most of those pilots is less surprising, since that ability relies less on training, but his ability to notice and exploit weaknesses, which absolutely none of these trained pilots seem to have, is still a little too impressive.
Finally, a significant portion of the anime ends up as a reflection on why wars start, what reasons people have for starting them, and how they can be ended. Both sides fumble around a bit, without seeming to have a way (or a desire) to strike at the other side's center of gravity (that term refers to something without which a country cannot make war). There are a few dramatic gestures and attempts to end the war by clearing up the confusion that shrouded the start of the war... but no, I'm not going to turn these hints into overt spoilers by saying how that turns out. Overall, I found the ending rather unsatisfying, although once again, it may be that the message the anime is trying to send isn't what I want to hear. I suppose I'll have to wait and see if the planned second season clears things up a bit, or merely weakens the themes of the first with a needless extension.
Either way, I highly recommend this anime - partly for the action sequences, and partly because I found it very thought-provoking.