Imagine an anime that's deliberately dialled up to maximum on bizarre plot developments. Theoretically it has a domestic real-world setting, with a boy and four girls living in a boarding house. Yuuta is the boy. Meika is their landlord, Rabura claims to work as a spiritual medium, Mikatan has pink hair and Ito is a teenage shut-in who refuses to go to school.
However this show also has robots, ghosts, spiritual possession, a planet-killer asteroid, time travel, superheroes, a talking cat, terrorist organisations, idols, causal loops to hurt your head and panty flashes that will destroy all life on Earth.
And that's the spoiler-free version.
The show's main problem for a lot of people might perhaps be how much it changes. At the start, it's just silly. Ep.1 is laugh-out-loud ridiculous. If Yuuta sees girls' panties, then he gets a fifty-foot nosebleed and superpowers, but if he sees them too much, an asteroid will wipe out all life on Earth. This happens twice. Time can be reversed, because SPOILER has been turned into a SPOILER. If you can take this seriously, get help.
It's quite fun, though. It's silly and featherlight, but successfully so. The main problem with this episode is its panty shots, although in fairness the show's hardly being surreptitious about them. They're in the title. "Punch Line" has nothing to do with superheroes or fighting, but instead means "panty line" and invites wordplay with "panty flash". Yes, that's right. In this show, fanservice is part of the plot. It's silly and funny, but in ep.1 might perhaps get a bit much, depending on taste. (The show dials it back a bit later on.)
Other things that happen later in the series include:
(a) a coherent and even ingenious explanation for everything. Yes, including the knicker-detecting extinction event asteroid.
(b) a plot. Yes, I was surprised too.
(c) an increasingly dark and serious tone. You might be wondering how this fits. Well, it sort of does. Global apocalypse is coming, almost everyone in the cast dies or is threatened with death and the show has a sobering viewpoint on going back in time to change things. (No, death needn't be permanent if you're Yuuta. However... well, SPOILERS.)
Can this show survive trying to combine apocalyptic silliness and a literal apocalypse? Personally, I'd say yes, although in later episodes the opening theme song did become an increasingly inappropriate contrast with the general tone. (I like that title sequence. I never skipped it. However it's a better fit with the show's goofy side.)
There's also unintentional silliness with the U.S. Army in ep.11, whose soldiers are either Japanese (speaking perfect Engrish) or very audibly from London.
It's a bit of an oddity. I enjoyed it, but you'll probably do your head in if you try to marathon it. However I like its cast and we learn quite a few intensely surprising things about them. It should also be emphasised that this show has a proper plot. It's mental, yes, but the show's taking it seriously (despite appearances) and you shouldn't expect everyone to be still alive at the end. I liked the way that the finale reminds us about things we'd forgotten in the madness. It's quite good. It's probably not quite strong enough to recommend to people, unless they're looking for something offbeat, but it's more serious than it looks and it's full of surprises.
If anyone ever asks you for an example of "only in Japan", show them this. It's more coherent, warm and character-based than you'd think from hearing people talk about it, but it's still a show where ghosts need to power up with cinnamon and might be the disciples of a sleazy cat who likes watching cat porn on the internet.