These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: During the live-action film, the villain suddenly appears at one point, singing a song with his henchmen accompanying on violins. Cutey Honey's facial expression at that point has become slightly memetic.
Complete Monster: Jewel Princess from the updated series is a Psycho Lesbian who runs a jewelry shop as a front for entrapping beautiful girls. When she finds one she wants, she has her brought to the basement, stripped naked and subjected to a gas that results in the girl being turned into a statue, so she can preserve their beauty and keep them around for her to admire. She even loves their screams of despair and pain as they're converted into statues. She forces the captive heroine Honey to watch as she does this to an innocent girl, and once Honey bests her in a fight, Jewel Princess takes a serum to change into a monstrous creature to simply rend Honey apart that way.
Re: Cutey Honey deserves special mention. Natsuko and Honey have two instances of Intimate Healing that involve naked cuddling and French kissing respectively, in addition to assorted other moments of Les Yay, and at the end of the last episode, Sister Jill ends up floating naked in a void and possessively hugging an equally naked (and unconscious!) Honey.
Periphery Demographic: Go Nagai says he was surprised when he found out that the series attracted so many female fans. Hence, the creation of Cutey Honey Flash.
Weird Al Effect: How many people have even heard of Tarao Bannai? That was the source for Honey's "Sometimes I'm a..." speech, which is now more associated with Cutey Honey than anything else, at least in the West.
The speech can also be heard in the first Cyborg 009 movie, which must be a Tarao Bannai reference and not a Cutey Honey reference because that movie, from 1966, predates Cutey Honey.