Round objects = balls. It is a Britishism.
Most Americans would probably be more familiar with Brit’s saying ‘bollocks’ in this context than ‘balls’, but since ‘bollocks’ and ‘balls’ (in the ‘testes’ sense) are synonyms, it amounts to the same thing. (And, yes, the joke is that Bernard and Hacker are both calling it bollocks with various levels of obfuscation, and Hacker going off script confused Sir Humphrey due to ‘objects’ (noun) being a homograph for ‘objects’ (verb).)
Just the other day I saw an ad for a t-shirt which had something like “Dammit Jim!” and then a bunch of icons for different icons, with all having a “no” symbol through them except a stethoscope. I thought it was cute.
Latka Gravas? :dubious:
Quite so. But the original obfuscation was, IIRC, “pointed tools of ancient shoemakers,” or words to that effect equaling “cobbler’s awls” (“balls”).
A transcript of the dialogue can be found here
http://en.wikiquote.org/wiki/Yes,_Minister
but that particular quote is quite a ways down the page.
Sir Humphrey Appleby - for it was he - pretends to misinterpret the joke, rather. He notices the possible double meaning and exploits it to score a point off Jim Hacker, that being one of his pleasures in life. There’s no way Sir Humphrey would not get the intended meaning.
Aha! Yet another layer of witty humor to savor! 
Nah, Bernard’s obfuscation was a layer deeper (or two, depending how you want to count) and with more idiom than that.
CGSM -> Consignment of Geriatric Shoe Manufacturers -> Load of old Cobblers -> Cobbler’s (Awls).
Indeed, quite correct! Jolly, jolly, jolly good! 
I never watched the Seinfeld Show, but I still know the saying “no soup for you”! I hate gangster shows and don’t even know which one this is from, but I still understand the saying “say hello to my leetle friend” and so on. One doesn’t have to be a fan of a specific show to have heard and assimilated very common cultural references.
DeForest Kelley, Dr Leonard “Bones” (short for “sawbones,” 19th-century American slang for a doctor or surgeon) McCoy on Star Trek-TOS (The Original Series), played a cowboy in so many shows that it might very well have been him.
Al Pacino in Scarface? :dubious:
Is everyone familiar with the book “Dammit, Jim” by Ima Doktor and Nada Brickleier?