Important things that happened

We learn from her mother that Yumeria's real name is Yamada Yuuko. Spelled "Yuko" on the cake.
Yumeria turns 24. The episode occurs on her birthday.

Monster of the Week

Kabuki Chou Mesuguro Hyoumonchou (Powered-up) 歌舞伎町メスグロヒョウモンチョウ（強化）
Voiced by Midorikawa Hikaru AKA Guririba, which is short for "Green Light River", a literal translation of his Japanese name.

Scientific name is Damora sagana. Kabuki-chou = Kabuki City. The pun here is that Chou is a homonym for butterfly.

It looks like he wears sunglasses in his powered-up form.

Super Sentai References

Kozukozu is dressed as Kai from Mahou Sentai MagiRanger. The theme song is also playing in the background during this.
She offers food to Akagi from Snack Gon (GoRanger), Snack Safari (Sun Vulcan), or Kyouryuuya (Abaranger)..
In Yumeria's room she has Girls in Uniform, a line of female Sentai figures.
Reference Denji Sentai MegaRanger episode when Chisato has to pretend to have a boyfriend.
Akagi laments losing out on a Bioman toy when the shop disappears.

Trivia

Instead of Yahoo! Japan, Hakase looks things up using Ugle! Japan.