Game Completion: In the middle of Part 3, Chapter 5
I really like the level design in this game. Each chapter feels fairly unique, with distinct objectives and complications. I can only recall one or two stages so far that are simple battles in which you just need to rout an enemy or defeat a boss. Interesting objectives are so common that, in one mission, the lack of any such complications made me rather paranoid that something would happen towards the end to make things more difficult (I admit I was rather disappointed when it turned out it was just a simple battle).
Some interesting things this game does in level design, especially compared to previous Fire Emblm games, are:
1) The different chapters have many kinds of Victory Objective. With distinct Rout, Defeat Boss, Defend, Arrive, Sieze, and Escape objectives, as well as few which are outside of those common types (like the objective of mission 3-3). Various creative uses of these objectives, especially the Arrive command (such as in mission 3-Prologue), keeps the stages from feeling repetative. Having multiple wining conditions, especially in the otherwise long and potentially boring Defend missions, is also a nice feature.
2) Most levels have some kind of incentive that encourage the player to stay on the offensive. The Fire Emblem games are easiest if you play cautiously and advance slowly, but are much more fun if you push as quickly as you can and push your ability to respond to attacks to the limit. This game rewards the latter by both traditional methods for a Fire Emblem game, like having Thieves and Bandits who will destroy towns and rob treasure chests if you progress too slowly, and a newer, but very common in this game, method of having civilians and allied soldiers on the battlefied who can be saved. As far as I can tell, keeping allied and civilian units alive and letting them escapape the battle rewards the player with valuable bonus experience in this game. There are even some stages which ask the player to avoid killing enemies, an interesting and novel challenge for the series. Previous Fire Emblem games might only have a single stage with nameless allies that need rescuing, and often you only receive an item for saving them, so the fact that they apear so often in this game is a nice change.
3) The actual terrain of the battle is often quite varied and interesting. The addition of different levels of height, and gaps that can be climbed, both add a lot to the game experience.
Of course, there are a few problems with the level design, mostly stemming from excessively powerful defensive locations, and terrain that is more difficult to traverse than is necessary. In a game where three-to-one odds can be fatal, one mission (2-Endgame) has a choke-point that allowed a single character on my side hold back a constantly spawning group of enemies which could number up to sixteen or more at a time, and in other missions the enemies hold almost equally powerful locations. Another problem is that heavily armored characters and mounted characters seem to be punished too much by rough terrain, especially gaps that require climbing. Armored characters already have less movement than other characters, and mounted characters suffer lower caps on their stats (and penalties on movement in indoor stages), so these characters end up being all but useless on some stages. At the same time, flying characters (who might be stronger and more common than mounted characters) don't suffer these penalties and are necessary to get through some stages with a large number of choke-points, so they end up being rather unbalanced with horse-riding units.
That about covers stage design so far... Before I forget, I should mention that I really like the addition of a mid-battle save (rather than just a suspend) to the fire Emblem series. It eases a lot of frustrations with replaying a mission many times to make up for a minor mistake, and permits the player to be more daring in battle (which adds to the effect of #2 above), making the game more fun.