Luckily, an anime's exploration of themes/subjects/whatever doesn't depend on whether or not its tone is unanimously consistent. Psycho-Pass has cutesy elements and I doubt anyone who's seen the show would dismiss the topics it tries to explore because of that.
You can do anything. Doesn't mean you should.
I can try to make a serious, somber funeral scene and have clowns parade trough it.
Clashing tones, clashing visuals do hurt a show. But it depends. Dependso n the show, the scene, the charactes.
That duck-creature work for One Piece because of the art style and general cartoony, childish atmosphere.
It wouldn't work in Cowboy Beebop for example.
Silly things can hurt the credibility of the story. When something goes out of it's way to look/sound/act childish, it's hard to not take it as such.
Take for example, the overy girly girls. Girls who are acting and dressing up far more girly than any RL girl ever would. Their presence can just be jarring, shattering their perception as a real character.
Or the overly cute loli's/things that really add nothing to the story. You could remove them or replace them with something else and the story would gain something from it, not loose.
If you want an example, that stupid retarded flaoting mini-bot (irritating as Ja-Jar) from Gundam 00 (the one with the Gundam Mesiters). Or the loli explosive expert from Scientific Railgun 2'd season.
Replace that retarded helper bot with a less annoying one.
Replace that loli with someone who actually look like they could carry and know a lot about explosives and be a friggin mercenary.
You get an overall better presentation and you loose little to nothing.