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.
A Youtube commentor pointed out something about Brain's analysis of historical figures, and how he was taking the wrong ideas from them, explaining his errors he makes even with analyzing history.
You absolutely need world alliances if you wish to conquer the world. Cleopatra committed suicide after Mark Antony (one of the leaders of the belligerent factions during the Last War of the Roman Republic and her lover) was killed in battle (Antony also had married Octavian's sister but continued his affair with Cleopatra, which strained tensions in the Triumvirate and got Cleopatra dragged down when Antony was). Largely, Cleopatra wasn't ambitious enough or present enough in Rome to match Octavian's efforts, and didn't identify which alliances would benefit her most. Allies are largely what got her so far in the first place. Shunning world alliances to try to command everyone's appliances would be a disastrous mistake.
Hannibal is one of antiquity's foremost military commanders. He lost in the end not because of any tactical error involving war elephants, but because the loss of support for the war back in Carthage and the attritive, guerrilla tactics the Romans used against him combined to gradually wear down his army until it was incapable of securing a major victory. If anything, Hannibal should be a lesson that you can't win a war without the support of your people back home to pay for and supply your armies in the field. In this case, Brain is correct that he can and should use the television to be admired if he wants to be successful, but in incorrect is discarding the foremost weapons of the time in favor of exclusively having popular support and political power (which contrasts with his conclusion from Cleopatra: that alliances and political maneuvering are unimportant to world conquest.) He's also wrong, in the facts anyway, since Hannibal more than made it past the Roman Sentinels, marching his army to attack from an unexpected direction and securing quick victories early on. It was only once he lost support for the war that things really went south.
The battle Attila fought against the "heroic Franks" could have been a much more decisive victory for the Roman-Visigoth alliance if the Roman-Visigoth alliance had seized upon the opportunity their battlefield victory provided. Attila was in an alliance with the Roman Empire, but a falling-out between the Hunnish Empire and the Roman Empire occurred when the Emperor's daughter sent her engagement ring to Attila (in order to escape forced marriage) and the Emperor responded by exiling her. Both sides then intervened on different sides of a Frankish civil war. At the deciding battle, the Romans arrived and attacked the Huns from the flank while the latter were attacking a city. The Romans routed the Huns but failed to pursue, and Attila went on to regroup and attack Italy (and was eventually repulsed due to a combination of disease and lack of supplies in Italy to resupply his army due to crop disease), and eventually died either due to political assassination or internal bleeding as a result of heavy drinking. Subliminal messages wouldn't have helped Attila, and pillaging like a criminal certainly had little to do with his demise. Watch your back and watch your health. He wasn't really a stereotypical barbarian, anyway.
Early on, Caligula was largely a progressive ruler of Rome, conducting many civil works projects and other civil improvements. He also had a habit of spending money to spite his political enemies, and generally increased the power of the Emperor. He wasn't particularly more corrupt than other feudal leaders in the beginning, but he did earn the enmity of the Senate for re-exerting Imperial power (there had been no emperor for a period of time before him). As his feud with the senate grew, his sanity deteriorated and his sense of self importance ballooned, ultimately involving himself in several political scandals and getting assassinated. Caligula is a lesson in how not to play politics and not to have an inflated sense of one's own importance (something Brain is critically ignoring). Maybe hypnotizing the senate and entire roman populace to forget the famine and his scandals would have helped ;].
Napoleon was defeated in Russia because his army not properly equipped to deal with the conditions. He was then exiled, then returned from exile, and they was defeated and sent back into exile at Waterloo. Napoleon was prompted to march to Waterloo to combat the rest of the world that was invading France in response to his return to power. Napoleon's fall did not come about as much through conquering with depravity as failure to have political allies to turn to to help him out. Napoleon made many strategic errors of the course of his career, though he did not choose to attack Britain; Britain was the aggressor in all the wars he fought against him (The wars in which France gained the enmity of the rest of the world occurred before he came to power, and they feared (correctly) that he would restore French power). He was too ambitious and politically obvious and not discrete enough. Undermining gravity would certainly not have helped, more political tact probably would have. From both Napoleon and Hannibal, one should also learn to be wary of guerrilla fighters, since Napoleon and Hannibal both suffered a large part of their eventual defeats because of enemy guerrilla tactics in Spain and Italy, respectively.
From Genghis Khan to Charlemagne and Alexander down to Tamerlane" were successful conquerors and leaders, their empires fell because an unclear line of succession left a power struggle. Alexander's empire dissolved immediately (split between his generals), Ghengis's was split between his son's generals, there was a power struggle between Charlemagne's grandsons after his son (who had succeeded him) died, and Tamerlane's other descendants all tried to seize power from his named successor. Essentially, if you want your empire to last, power cannot be entirely consolidated in you (which seems to be the opposite of what Brain is trying to do).
Perhaps it is a hidden message of 'you can study history, but you can easily learn the wrong thing from it'.
Pinky and the Brain are lab mice. And they're still living in the lab.