The Disappearance of Nagato Yuki-chan (TV)

In episode 1, the 'weird tune' Asakura is humming in the kitchen as she's making food is Hare Hare Yukai, one of the closings to The Melancholy of Haruhi Suzumiya.

In episode 1, during the cooking at a restaurant challenge, they are parodying the original Iron Chef series. Asakura is dressed in the blue uniform of Iron Chef Japanese Rokusaburo Michiba, and Tsuruya is dressed in yellow as Iron Chef Chinese Chen Kenichi. Kyon also does the Chairman's signature move of biting into a yellow bell pepper.

In episode 1, the music playing during the opening credits is "Pavane for a Dead Princess" by Maurice Ravel.

In episode 3, when Kyon is hit by the frog costume's head, Mikuru comes to see if he's ok, but he peeks at Mikuru's panties, and then Haruhi says something like "It's 265 million years too early for you to peek at this cute girl's underwear" (22:43). Haruhi said the same sentence on Disappearance of Haruhi movie (12:52).

In episode 4, Haruhi and Tsuruya are about to battle around 1:20. In the background, they show Haruhi as a dog and Tsuruya as a crane. This is in reference to The Melancholy of Haruhi-chan Suzumiya.

In episode 6, Kyon takes away the game Yuki is playing, allowing the viewers to see the game. Yuki seems to be playing on a PS Vita and the character on the screen looks a lot like Michiru Matsushima from the Grisaia no Kajitsu games.

In episode 7 around 4:10, Haruhi mentions how doing summer homework after having all that fun would ruin the fun. This is a reference to The Melancholy of Haruhi Suzumiya's infamous "Endless Eight."

In episode 8, Mikuru sings a song called Mitsukete Happy Life. That is actually Mikuru's Character Song from The Melancholy of Haruhi Suzumiya OST. Meanwhile, Kyon sings a song called gira gira SHAKE (Glaring Shake) which is a parody of a song called Ultra Soul by B'z

In episode 10, at about 13:03, Yuki shows Kyon the title of the book she is reading. The book is “Le mystère de la chambre jaune” (The Mystery of the Yellow Room) by Gaston Leroux. The book is considered one of the first locked room mystery crime fiction novels. Later in the same episode, at about 14:55, she shows Kyon the title of the book she will read next. The book is “Le Parfum de la dame en noir” (The Perfume of the Lady in Black) which is the sequel of The Mystery of the Yellow Room. This is a reference to the Remote Island Syndrome arc in Suzumiya Haruhi no Yuutsu TV anime where a murder takes place in a sealed room.

In episode 11, at about 17:32, Ryouko tells Kyon that if her stress surpasses a certain level, she might end up stabbing him. This is a reference to the scene in Suzumiya Haruhi no Yuutsu TV anime where she really attacks him and tries to stab him (the episode in question is Suzumiya Haruhi no Yūutsu IV)

In Episode 16 around 4:20, Haruhi is humming Bouken Desho Desho, the first theme song to The Melancholy of Haruhi Suzumiya

In Episode 16 after the ending credits, Kyon and his sister are watching a baseball game when Haruhi unexpectedly calls. All while Kyon feels something isn't right. This scene and the scene that follows is almost identical to that found in The Melancholy of Haruhi Suzumiya's "Endless Eight"