I tend to be very nitpicky with my own stories. I write with the spell checker on and go back a couple of times to check for anything it missed before posting stories online.
As for other stories, people are human, so if someone makes one or two errors in a story and they don't interfere with the flow, it doesn't bug me.
If the story is badly written and there are dozens of typos that a spell checker or decent beta reader would have caught, and I'm reading it on a site like fanfiction.net, then I might say something like "You might want to get a beta reader." But I won't point out every little thing they did wrong. IMHO, beta readers are the ones who are supposed to nitpick and point out everything before the story is posted.
I am also way more nitpicky about published writers and professional journalists. In fact, I e-mailed my local paper when they had a typo in one of their headlines on their website the other day. It was the kind of thing a spell checker would have caught. I have also found typos in published novels and cringed. I think the standards for professionals are higher, though.
As for constructive criticism, I don't mind when people nicely point out something obvious so I can fix it. However, I'd rather get feedback on plot, characterization, etc.
