The series is a metaphor for transsexuality that is more interesting than most in that it can be viewed in two different directions: Ash is either an MTF in denial, or an FTM who isn't accepted as such. Especially this part. You can't really put it much more clearly than someone being filed in the wrong section, but the first line of the writing says "male." Also, probably the latter, given that he's forced to dress up in clothes that don't really suit him, and actually into girls.
Rumisiel's comment about how "With Vashiel's powers bound for his vacation, I get to be the stronger brother" seems confusing. Why would someone in exile be given less restrictions than one on a sanctioned vacation? However, Rumi has never done anything bad with his angelic powers (he hasn't done anything good, either, but still), while the last time they let Vashiel run around free he nuked a city. Of course they'd make sure Vashiel is bound, while not particularly caring about Rumisiel. Remember that heaven in a bureaucracy, as well. Vash's abilities as heaven's official briefcase nuke are probably considered a company asset, where Rumsiel's never considered an asset of any kind by anyone.
People mention the relevance of Vashiel's truth bond in terms of the one time he threatened Cassiel. What about when he insults her?
The comic becomes increasingly sympathetic to those of transgender as it goes along, which at first may be interpreted as the comic and it's author "maturing". However, when one thinks again about this one realises that the comic isn't becoming more sensitive, the characters are. When Ash first wakes up he is disgusted at himself, and immediately wants to be a boy again. However, as the story progresses Ash, and by the effects of socialisation Emily, become more accepting of the fact that he, at least for the time being, is a woman, even if he still has every intention of turning back.
Readers seem to be a bit more obsessed with the gender-bending aspects of the storyline and forget that it's a story about a bratty, sullen teenager's coming-of-age. It's pretty clear from page one that Ash becoming an actual adult about a variety of things is going to be the main plot arc, and getting over an obsession with traditional '80s high-school comedy gender roles is just going to be one relatively minor aspect. For instance, it wasn't really a surprise that adjusting his attitudes toward his parents would figure prominently.
A mentioned in this post, think about how many people were affected when the Misfile happened. All those people now no longer exist and have been replaced with clones of sorts. Most obviously "Girl-Ash" who has a whole "life history" but doesn't fully exist. As far as we know, there is nothing special about Ash or Emily that would make them more prone to being misfiled, a gender swap is pretty mild compared to the example Rumisiel gave when he explained the system, and Rumisiel was in the least significant section of the file. Can you think of anything more terrifying than living in a universe where every aspect of both your existence and the very foundation of reality can be changed at any time, by negligence or malice on the part of beings you'll never even know about, and if the change is about you personally you might be literally stuck in someone else's life?
There's also the concept that as soon as the misfile is fixed one way or another, history will change to fit that scenario. Essentially, the characters the comic follows are just deciding which parallel timeline will exist after the correction- they'll basically cease to exist at that time.