Anachronism Stew: Justified in that Celcia's spell summons objects from our world to hers (so having a tank makes perfect sense and is awesome), but also played straight in the pop culture references and the many religious profanities used. And Elf Mc Burger. You cannot escape Mc Donalds.
This eventually becomes a plot point.
Attack of the 50-Foot Whatever: Creative use of an enlargement potion in an absence of Magic Pants makes for instant nudity. It also makes for an angry giantess who punches out a dragon that is threatening her town.
Badass Crew: For better or for worse, Junpei, Airi, and Ritsuko and later Celcia are a team.
Can Not Spit It Out: Seriously, people. "Hey, my friends and I are looking for the fragments of a very powerful and important spell that has imprinted on five random elf women. You don't happen to have any odd marks that popped up recently, do you?" IS THAT REALLY SO HARD?!
They've tried. It didn't work. Elves can be such snobs.
The Chick: Airi. Not that she's ineffectual. She just doesn't do a lot of the fighting.
Clingy Costume: Episode 10, season one. An elf kight comes to the group and asks for help removing it.
Cool Tank: The Type 74 tank, practically a character in its own right. Later on, it actually does become a character, when the cat spirit Mike (mee-kay) possesses it.
Critical Failure: Celcia, a lot. She screws up the spell to send the trio home not once, but twice. Not only that, but she's the one who cast the spell that summoned Junpei, Ritsuko, and Airi to her world in the first place! Despite exemplifying this trope for the sake of the plot, she's reasonably competent when the stakes aren't returning the heroes home.
Guile Hero: In addition to being a Master of Disguise, Airi is skilled at reading people and controlling them. She can often do more with a few words than the others can do with magic, bullets or fists.
Magic Misfire: Celcia disguises herself as a doglike creature to try to help them find the spell fragments without being recognized. However, when they find the first fragment and she transfers it to herself, it causes Shapeshifter Mode Lock until they have all the fragments. Her increasingly ridiculous appearance as the spell fragments transfer to her become a Running Gag.
Paper Fan of Doom: the women in the main cast, usually directed at Junpei (or any male too obsessed with the Elf Hunters quest), although Junpei himself uses it to prevent an uncomfortable old man homoerotic moment.
Playboy Bunny: Junpei accidentally bursts into a room where girls are dressing into them.
Potty Dance / Potty Emergency: Junpei, Season 2 Episode 2, complete with a graph and flashing alarm showing his current state. His dilemma leads to some uncomfortable images. Ends with the discovery of a teddy bear that can excrete toilet paper, in perfect rolls, complete with cardboard tube.
Sapient Tank: The type 74 "Mike" after being possessed by a cat.
Save Both Worlds: Brought up explicitly near the end of the first season is the idea that both Earth and the magical world to which the cast has been sent are fundamentally connected and in danger of some sort of magical cataclysm if the cast are not sent back to Earth. Then averted, or maybe just forgotten by the writers, because it's never mentioned again.
It's possible that the worlds' combining only happens to a limited degree when one casts the summoning spell, and the additional combination witnessed during the first season was a combination of our heroes Walking the Earth and Annette's use of the summoning spell.
Schizo Tech: There isn't really much of a difference from the real world other than that everything runs on magic instead of technology. Yet for some reason police and guards still use swords when there should logically be some kind of magical firearms technology.
Stable Time Loop: It turns out that the Big Bad whom Celcia casts a protagonists-summoning spell to defeat is amnesiac Celcia from the future.
Summon Everyman Hero: The back-plot of the story: to defeat the Big Bad, Celcia casts a spell which summons the protagonists. Less than a minute later, the Big Bad is only mostly dead, thanks to Ritsuko blasting it with the armored tank that the spell also brought along.
Voluntary Shapeshifting: Celcia can transform into whatever she wants with her ring. However, played with in that she always ends up transforming into animals (hence she is considered Team Pet) and cannot transform back once she absorbs any one of the spell fragments. She can only change back once she gains all fragments or lose them all. The fact that the spell fragments, which manifest visibly in her body as she gains them, make her look ridiculous◊ does not help. For those who don't understand the image, the dark lines on the big bird are the spell fragments that manifest on Celcia's body. And that big bird is only one of the forms that she ends up not so willingly taking throughout the whole comic.
Wrong Genre Savvy: In one chapter of the manga, Junpei states that "you can't go by in a fantasy world without knowing a spell or two", and thus sets out to train in the arcane arts in his very own way. Hilarity Ensues.