The best stupid sitcom characters aren’t actually stupid at all. They have an intelligence with a flawless internal logic.
Take Baldrick for example. In his two most memorable scenes, he’s not wrong, and his logic is impeccable.
Especially in this.
Something else that makes a ‘stupid’ character more intresting is to have them being inexplicably brilliant at their job. Bubble in Absolutely Fabulous pulls this off, and even manages to rake in some extra cash by blackmailing Edina and Patsy.
Alice in The Vicar Of Dibley likewise has a precise and insightful world view which she uses to pick apart crap pub jokes.