You describe some dire, humorless Quora, not the one I use. I've seen plenty of misspellings. Founder (and Harvard grad) Charlie Cheever used "its" instead of "it's" several times in one answer. I've made typos that I went back and corrected myself.

Humor:

https://www.quora.com/Ultimate-Frisbee/Is-it-possible-to-pla...

https://www.quora.com/Marc-Bodnick-1/Does-Marc-Bodnick-ever-...

https://www.quora.com/Chief-Executive-Officers/Who-is-the-mo...

Casual subjects:

https://www.quora.com/Hipsters

https://www.quora.com/What-Ani-Is-Wearing

You can answer anonymously, but you have to register.

There's sheer irreverence in some of the boards (new feature, non-Q&A posts):

https://www.quora.com/DeathByPuns

For something completely freeform and casual, Yahoo Answers exists (I've actually found useful answers in it too, rarely).