Good poll, especially for this site. - Edit 1
Before modification by Joel at 05/10/2011 08:12:51 PM
1. Does anybody (besides me) use proper grammar when texting, posting on Facebook, etc.?
I try, usually, because poor grammar annoys me in itself, and also because I know Timbekah, TVoLT, Legolas and Camilla have impeccable grammar and hang on my every word.
Sometimes I feel like one of them is watching over my shoulder as I type and I want to avoid embarrassing errors like confusing "e/affect." It would be bad enough with an American or Brit, but there is nothing more shameful than having ones grammar corrected by a person speaking a second language. 
2. Do you correct somebody who uses incorrect grammar while talking? If not, do you at least do it in your head?
In my head, yeah; it is rude to correct people speaking to you.
3. Do you wince whenever you read a particularly awful Facebook post?
Frequently.
4. Have you noticed a trend on Facebook where people don't even bother using periods to separate sentences anymore?
Sadly so.
5. Have you noticed misspelled words that have nothing to do with 140 character length? (Today I saw somebody spell "do" as "dew"
Yeah, but that is a common lapse having little to do with grammar. I long ago noticed that my likelihood of confusing homophones is directly proportional to the extent of my drunkenness and/or sleep deprivation at any given time. In reviewing this response, I noticed that I initially used "no" instead of "know" a few questions below this one, and not for lack of knowing the difference. Whether carelessness is more or less excusable than ignorance I leave to your discretion.
6. (Off topic) Are people whiny bitches on Facebook or what?
That is among Facebooks primary purposes, if not its chief purpose.
7. Has anybody ever called you a Grammar Nazi?
Lots of times; I am a founding member of the Society for Better Spelling and Grammar (AKA the BSG, because we mispell our own abbreviation.)
8. Has Twitter and texting eroded proper grammar for today's youths?
Almost certainly. To be fair, however, the process began long ago when "Grammar School" ceased to be more than a name. In twelve years of US pre-secondary education, only one of my English teachers taught the parts of speech exhaustively. As a result, many Americans have to be told what "never end a sentence with a preposition" and "do not split infinitives" even MEAN. Most people know what a verb is, but far fewer know what an auxiliary verb is.
9. Have you succumbed to the 140 character shortcuts? How often do you text or tweet this way?
No, and never. It is all I can do to fit a synoptic subject line within RAFOs 99 character limit.
10. Were there any grammatical mistakes in this survey?
Probably. Technically, I believe the currently accepted STYLE (not necessarily the same as grammar) is to omit commas before the final element in a series ("x, y and z" not "x, y, and z,") so it could be argued there should be no comma before "etc." in your first question. I still dislike the word "besides," but that is my idiosyncracy, since it is undeniably correct grammar (I prefer using "beside" in all instances, which is also acceptable, but vulnerable to the ambiguity discussed here.)