Cliché Storm: The amount of tropes played straight is a little overbearing at times.
Covered Up: The soundtrack features a cover of "Joining A Fan Club", originally by Puffy songwriter/producer Andy Sturmer's early-1990s band Jellyfish.
Counterpart Comparison: The show itself is often compared to the anime Panty & Stocking with Garterbelt. Both feature a duo of two girls with different personalities and interests, a man who at least works with them and a seemingly typical mindless pet, with them living in the same residence. Oh, and we didn't forget that both of the shows also feature a plot-relevant villain (two, in this case for Scanty and Kneesocks). They also have uses of an art style from opposite sides (i.e. this show uses an Animesque style, while PSG has an art style looking like Animesque Western AnimationThe Powerpuff Girls), and are also seemingly wacky.
It helps that this show struck inspiration for the anime.
Ear Worm: The background tunes will stick in your head for days on end.
Unexpected Character: The Talent Suckers' cameo appearance in "Puffy B.C.". That episode took place entirely in the pre-history and they only appear because of a never seen before (or since) Time Machine.
We're Still Relevant, Dammit!: The show hit a twofer with this. Puffy AmiYumi were way out of their peak popularity when the show landed, and it also came in the dying wave of anime-parody/anime-referencing western toons.
The Woobie: Both Ami and Yumi can be this at times. Episodes like "In the Cards" and "House Unkeeping" are seen as their most woobie-ish moments.
Jerkass Woobie: Kaz is this when he has to put up with Jang Keng and Tekirai (Ami and Yumi's pet kittens).