Well, sure, I would have liked more info on its origins (though primarily through a brief explanation of Snokes entrance into all this), but my bigger issue with the First Order (and the Resistance) is its lack of characterization.
The Empire was very well characterized both through characters and through smart exposition via dialogue. First, characters like Tarkin and his council in ANH, the various Admirals, general and lieutenants, and then Vader and Palpatine, helped to characterize the Empire as a martial regime concerned with maintaining order through force and fear. At the same time, through dialogue ANH defined the Empire as a increasingly totalitarian government at least partially restrained by a nominal Senate, with a growing number of revolting systems. We got a sense for how the Empire ruled through this dialogue and through the larger motivations for the Death Star.
We havent gotten anything of the sort with the First Order, except for Huxs speech about the Republics abstract acquiescence to disorder. We have not gotten a sense of what the First Order fundamentally is, and therefore the actual threat it poses. Weve also only focused on three characters, who are so personality driven that they only really represent themselves, and not the organization to which they belong. This has made the First Order quite hollow to me, which is made more so by the fact that the First Order essentially looks like the Empire. Its as if the First Order is the reanimated corpse of the Empire, without its soul. I feel the same way about the Resistance.
This is one of the reasons why Im much more partial to Rogue One, despite its poorer character portrayals: that film seems to capture the heart of the Rebel Alliance and the Empire, while adding nuance to both.
Anyway, I think the First Order could have actually been portrayed as a darker, more sinister version of the Empire - the cruelty and horror and violence without the order and governance and stability. That the First Order steals and turns children into indoctrinated, nameless stormtroopers could have been portrayed in a way that made the First Order stand out from the Empire (more 1984 than the latters German/British Empire). And with Kylo Rens genuinely terrifying ability to freeze people in place and probe minds, you could very much have had a much more fearsome threat. Snoke, of course, would then have been the head of that, rather than what we got.