This is the location in the office where reside the knowledge workers who care about language, accuracy and truth and who know their subject matter inside out. It is friendly rather than pejorative, and unless the residents turn into grammar nazis they are likely to be regarded with fondness.
There is no apostrophe: it is more a "corner of pedants"* or a corner where the pedants may be found than a corner that belongs to the pedants. This also allows the phrase to accommodate the possibility of one pedant or many, depending on the company or organisation in question.
*almost a collective noun?
Murphy's note: the pedant is most likely to be embarrassed by the hasty typing of pendant, itself an interesting word.
Nice try there, with that little preemptive feint about the apostrophe, but do you really think you're fooling anyone? Your reasoning about the possessive is faulty; Pedants' Corner needs the apostrophe corresponding to the possessive plural. Recall that the location in Hyde Park where people sound off on various topics is Speakers' Corner, not Speakers Corner (The Times of London Style Guide).
Normally I wouldn't be so obnoxiously snotty about a missing apostrophe, but this particular term more or less invites us to unleash our inner pedants. Not that anyone on Wordie needs much encouragement for that to happen.
Indeed it does (invite unleashing), and I'm not at all unsympathetic! In this case I am - as is probably evident - driven by pragmatism more than anything else. But I am also very pleased to announce that my particular corner has just recently become a true pedants' corner.
Not unrelated are all those church and place names that have come to assorted conclusions about the possessive. For example: in the Blue Mountains west of Sydney there is a spectacular lookout named after William Govett: Govetts Leap (no apostrophe). And no, he didn't jump, he just surveyed the spot (a "leap" apparently is a Cumbrian word for waterfall).
This debate has already raged on the Private Eye letters(') page: the suggestion that 'pedants' was an attributive noun was shot down with the observation that normal English attributive nouns are singular. However, one reader noted a number of counterexamples in common usage: 'sports field', 'games room', 'languages lesson', 'classics courses', 'Beatles records'.
The editor killed the debate just after someone had claimed that the possessive form is correct only for actual possession; to quote his letter: '"Visitors book" (no apostrophe) is a book for visitors to sign... However, "Visitors' book" (with apostrophe) is possessive and denotes that the book is the possession of the visitors, which is unlikely.' Trouble is, when I quote from 'his letter' (possessive), obviously I mean the letter he wrote and sent to the magazine, not one still in his actual possession.
'Pedants' Corner' seems the safest option; Private Eye settled on Ped'ants Corner to annoy everyone.
I still prefer "Pedants' Corner". But the point about place names is an interesting one. I've read somewhere that the correct spelling of "Pikes Peak" in Colorado lacks an apostrophe by legislative fiat - a special meeting of the state legislature was held in 1978 to decide the issue.