General lack of intelligence:
* Stupidity
* Dullness
* Ignorance
* Foolishness
* Simple-mindedness
Lack of cunning or resourcefulness:
* Naivete
* Simplicity
* Gullibility
* Unsophistication
Lack of wit or humor:
* Clumsiness
* Awkwardness
* Ineptness
Lack of insight or understanding:
* Blindness
* Obtuseness
* Insensitivity
* Unintelligence
The best antonym for "cleverness" will depend on the specific meaning you want to convey.