An old Pinky and the Brain comic, parodying Humongous Mecha anime, featured a scene in which Snowball the hamster and the titular duo charged one another in dramatic silence. The phonetic gag seems obvious now that one writes it out, but to a child it was incomprehensible.
The opening and ending of each show shows that Brain spends each day coming up with a plan for world domination that he then executes each night. It's no wonder then that his plans are often heavily flawed and fail, given that he only spends a few hours a day coming up with one, and as a lab mouse likely while being experimented on at the same time. In fact, it's impressive that so many of Brain's schemes seem plausible and sometimes are only seconds away from success before failing given those conditions.
Also, if he's spending the nights executing his plans and the days brainstorming and getting experimented on, he's probably not getting much sleep.
A possibly unintentional example, but one that hints at Pinky being smarter than he appears: In one episode, he quips that the book Jurassic Park would make "a great movie". This could be a jab at Pinky's intelligence...but given the fact that the book and the movie have many major differences between them...
It could be possible that Pinky's stupidity can be caused by Brain. Brain is often violent to Pinky whenever the latter does/say something stupid. It is possible that Pinky had suffered one too many conks in the head that hindered his intelligence via head trauma. Could dip in Fridge Horror territory.
Almost plausible, except that Brain goes through just as much damage as Pinky, and still retains his intelligence.