In the short story "The Inferiority Complex of Old Sippy", Bertie's Zany Scheme involves making sure that Sippy's old headmaster walks into Sippy's office covered with flour. When he announces this desired outcome to Jeeves without explaining the plan itself (booby-trapping the door), Jeeves' response is, "But why should he pursue such a course, sir?" It's a funny line in itself, but when you think about it, it also displays Jeeves' psychology. Bertie—and the average reader—would think in terms of traps and pranks when it comes to covering someone with flour, but master manipulator Jeeves instantly wonders what he could do to make his victim want to cover himself with flour!
For another subtle example of Jeeves' control, look no further than "Jeeves Takes Charge". Bertie explains that he fired Meadowes, the valet he had before Jeeves, because he caught him stealing his socks, "a thing no bloke of spirit could stick at any price". The cleverer Jeeves, on the other hand, is constantly inducing Bertie to give up some item of clothing or other, to the point where he can steal things from him—including socks—and give them away without retribution. (See "Jeeves and the Chump Cyril".)
As of Thank You, Jeeves, Brinkley is at large. And since Bertie never got near enough to technically fire him, he could show up at the flat at any moment! Let's hope Jeeves qualifies as a bodyguard...
Jeeves' constant manipulation of Bertie, despite being Played for Laughs, can get creepy if you think about it too hard. If we're to judge by "Bertie Changes His Mind", a lot goes into a typical Jeeves scheme that Bertie must never find out about, which means that in any given story Jeeves is probably doing even more morally questionable things to attain his ends than we're presented with. Plus, in Thank You, Jeeves we see him smoothly convincing J. Washburn Stoker, to whom he'd just been employed, that he freed Bertie from the yacht to get Stoker out of trouble. That's the kind of logic he uses on Bertie almost Once per Episode, but when he's doing it to some other sucker and not Bertie—and by extension, the reader—it's way more apparent that he's lying like a rug.
As TV! Jeeves and Wooster takes place in Christie Time, all Wooster's fun-loving chums are heading towards seven years of hell in World War II. You can't help but love the characters a little bit more when you think about this, and feel they deserve their fun while they can get it. (There are one or two references to World War II in the past tense in the novels, so essentially it got Hand Waved by Wodehouse.)
There are some references to how World War II specifically affected the English aristocracy in Ring For Jeeves. William Rowcester, the 9th Earl of Rowcester, works in a department store. Bertie is absent from the novel because he's attending a school that teaches members of the aristocracy how to cook, clean and do chores. Bertie is doing it as a challenge to Jeeves while other members of the school are doing it because they can no longer afford servants and have never learned to take care of themselves.
Then there's the theory that the whole Wodehouse canon exists in an Alternate Universe where Bertie's generation - especially those of Bertie's class - were never decimated by World War I, leaving only a few physically and mentally damaged survivors. If Bertie is in his 20s and 30s through the interwar years, he's of the generation that, in reality, lost the Edwardian 'innocence' that P.G. remembered them having in his youth. In reality, most of the Drones would have been killed in the trenches in their late teens and early twenties, and those that survived would no longer be terribly jolly.
Perhaps this explains the behavior of the men we do see. They aren't twits out of inbreeding or lack of real-world experience; they're psychologically broken.
Contemporary critics pointed out that Wooster's breezy prose is at odds with his clear idiocy. It's chalked up to Rule of Funny.
Also, "Bertie as a byword for idiocy" is a mild case of Flanderization; while he is far from a genius, Bertie as depicted in Wodehouse's original stories is not a total moron, and is often able to get halfway to a solution before Jeeves has to assist.
Bertie often forgets words in the middle of sentences (hence the near catch-phrase 'if that's the word I want'). Add to that the fact that Bertie is an educated gentleman (idiocy does not necessitate inarticulacy), and his prose seems not that unrealistic. Note Bertie's writing as taken from Much Obliged, Jeeves. Why critics might think this is too sophisticated is perplexing:
"What's the word beginning with dis? Disembodied? No, not disembodied. Distemper? No, not distemper. Disconcerted, that's the one."
Also, a lot of people who act stupid in general probably could be a lot more articulate if they had time to think over what they were saying. Bertie acts like an idiot in the stories themselves (and that's often because the situations he's in become too much for him, as they might for, well, anyone), but in the narration he's able to take the time to say what he wants to say. Everyday conversation doesn't allow for that, and having just backspaced my own words about twenty times in favor of better ones, I can sympathize.
Bertie's really not so much "stupid" as he is forgetful and weak-willed. Neither of those things preclude one from being intelligent.
It might also be a case of Unreliable Narrator, with Bertie exaggerating his mental inadequacies out of humility or for some other reason.
At the end of the first short story, "Extricating Young Gussie", Bertie and Jeeves settle down for an indefinite exile in New York City, and they remain there for the entirety of My Man Jeeves (at least a year, as mentioned in one story). In The Inimitable Jeeves, they're back in London, with no explanation given as to why they decided to return. (Made even weirder by the fact that they try the "escape Aunt Agatha's wrath by staying in New York" tactic again in that book, with no mention made of their previous stay.)
How did Bertie ever meet Rockmeteller Todd? This is a guy who lives on Long Island in the middle of nowhere, rarely leaves his house, and wouldn't go out partying in New York City on his own impetus in a million years. Even if there is a chance that they ran into each other while Rocky was delivering his poems to a magazine or something, why they'd like each other enough to keep in touch (and stay at each other's houses) is a little inexplicable.
Bertie mentions that his friends in New York include both wealthy socialites and starving artists. He likely was introduced to Rocky by one of these artists when Rocky was in New York to meet his editor.
This could be just a bit of Early Installment Weirdness, but in "Extricating Young Gussie", the family name seems to be Mannering-Phipps instead of Wooster. Unless there's some complicated explanation as to why Bertie's cousin on his father's side has a completely different last name from the rest of the family...
"Mannering-Phipps" was Bertie's original last name. If the story refers to Bertie as "Bertie Wooster" there's a chance it (as his cousin's name) was simply missed out in editing the stories for a newer edition; if it doesn't, then it's just one of the older stories in the original.
Or Gussie could be the son of a sister of Bertie's father.