Season 1 was great. I liked it so much that I gave my brother the DVDs for Christmas. It came 9th in Newtype's list of the most popular anime of 2013.
Season 2 didn't appear for another nine years and it's garbage. The main point of fan disagreement is whether it's bad, or merely less good than Season 1. Well, I can answer that. It's terrible. I got bored and stopped paying attention. Googling the original light novels, I found this comment on a web page about it:
"Below is the cast of the light novel and anime The Devil is a Part-Timer!. As a work in progress, beware spoilers. Or don't. This light novel is not exactly the most serious thing ever."
...which makes a lot of sense to me. The basic premise is that a Demon Lord, his generals and his heroic opponents have all been booted to our world and have to work in call centres and/or in McDonald's. They don't have their powers and they don't have any money. They have to live in a cheap apartment with a disturbing landlady and watch every penny they spend.
This is funny. Season 1 is starting from scratch and finds a lot of laughs in our demonic anti-heroes adjusting to their new lives.
Season 2, on the other hand, starts with a status quo and never really finds anywhere else to go. Its only idea for a continuing storyline is "more angels and demons want a fight!" This gets boring almost immediately. Our heroes already outrank pretty much everyone in their fantasy realms, so they can stop half the demons in their tracks just by telling them not to be silly. As for the legions of Heaven, they're more trouble to get rid of... but they're also so good-natured and laid-back that they'll just show up, waste our time for a while and then wander off again.
Our heroes don't really develop. Maou (the Demon King) and Emi (the hero who fought him) become surrogate parents of a cute magical child, but that just gives them additional responsibility without propelling actual stories. Chiho Sasaki is still in love with Maou while the prickly Emi isn't interested in him as a person, but the anime doesn't dare get them together because apparently Maou-Emi is a fan-favourite couple and the original light novels kicked up a storm by having him ultimately choose Chiho instead. (Although the way it was done was apparently clumsy enough to annoy even some Maou-Chiho cheerleaders.)
There's almost nothing here. If you watch the episodes, you'll find vanishingly little content in them. Demon/angel power plays, yes. Character-based storytelling that says anything about our protagonists, no. The anime's got a bee in its bonnet about why Maou tried to conquer the world and killed thousands of people, but it's just trying to explain away a contradiction. The Maou we see here is a trustworthy nice guy who'd never do anything bad and doesn't challenge the audience. Does this fit his backstory? Nope. Would this have been a better show had it embraced the concept of demonic heroes, at least to some degree, and pushed us a little out of our comfort zones? Obviously, yes. But that's not the show we're watching.
Sometimes, the show seems to run on sitcom logic. In ep.21, the demons go somewhere without the Heaven Girls... but they coincidentally show up anyway.
There are good bits. Occasionally, the show made me laugh. I also liked Emi's human colleague Rika, who fancies Alciel but knows nothing and is locked out of the loop. There's a good discussion in ep.25 that ends in "we'll tell Rika that we're demons from another world and then it'll be her choice".
Ultimately, though, it's a waste of time. It's spinning its wheels. It's out of ideas for how to follow up on its own success. Maybe, perhaps, possibly I'd have enjoyed this more had I first rewatched Season 1, to reestablish my love for the characters... but I'm pretty sure it would still have bored the arse off me.