Learn English – “Excel at something” vs. “excel in something”

There is no reason why the expression take measures (take action to achieve a particular purpose) cannot take a modifying adjective. Take (adj) measures should work with any adjective. (If a word modifies a noun, it is an adjective.) So Take control measures is okay.

I wouldn't use any of the five suggested terms. Three of them—"intellectually impaired," "intellectually deficient," and "intellectually inferior"—have obvious and unfortunate connotations of congenital mental deficiency that might suggest to some readers a eugenics-based arrogance on the part of the speaker/writer. There is no upside to being viewed as such a speaker/writer.

"Intellectually exiguous," although it enlists the mediating influence of the $3 word exiguous, still amounts to saying "intellectually inadequate," which again introduces the notion of innate intelligence or stupidity. "Intellectually meager" is the most creative option of the five, but it comes across as a bit odd—much as "intellectually sparse" or "intellectually skimpy" would.

In my view, a quasi-physiological critique is not necessary or desirable in characterizing the kind of "stupidity" that seems to be at issue in the sentence "Who can use the most Propaganda in their advertisement without the intellectually [chosen word] majority noticing?" As any good dictionary will affirm, stupidity can refer to poor judgment or to dulled perception as readily as it can to a shortcoming in raw intelligence. Rather than challenge the mental capacity or mental competence of the decried majority, I would focus on their slothful or submissive intellectual habits or on the state of disuse of their critical faculties. Along those lines, you might use one of these options:

intellectually indolent

intellectually docile

intellectually tractable

intellectually suggestible

intellectually reflexive

intellectually numb

intellectually anesthetized

intellectually etherized

There are many other options of a similar kind, none of which will make you sound like someone who is preoccupied with the idea of possessing a superior share of genetically inherited intelligence.