I haven't cosplayed much outside of cons, though I've seen some pretty hilarious reactions to some of my costumes XD (especially the time I went in cosplay from a con to get Chinese food XD). Really, the only time I've cosplayed outside of a con is for the cosplay parties for my anime club and for the Madoka Magica movie premiere that I went to in D.C. last year.
Mostly, people just stare at me, and I've gotten to the point where I don't care anymore. I really played it up when people on campus were staring at my pseudo-Lolita cosplay (wasn't much-just the fascinator and Irish walking stick that stuck out), playing the Victorian gentleman image up .
And yeah, people took my picture at the movie premiere, or stopped to talk to me about my costume and character (I was at a mall on a Saturday around the holiday season, so yeah, there were lots of people).
And soon, my anime club is doing a cosplay cafe (basically a non-sexual maid cafe) so I will be cosplaying in public then .
As for who I've been in public I've worn a kimono and a pseudo-Lolita look. I've been Chiyo-chan from Azumanga Daioh (for anime club only), Ib from the game Ib (anime club, cosplay cafe), and Homura Akemi (anime club, Madoka Movie premiere). I'm looking forward to everyone's reactions when I bring out the Sachiko Shinozaki cosplay from Corpse Party for the next cosplay party XD.
The short answer is yes to both. I've been cosplaying a few years and usually in very public places. You are going to find people who are ignorant in those situations.
Mostly non cosplayers who know nothing about the hobby will say things like "Oh, is it Halloween already?" Or snicker. My friend and I trolled those people right back, freaking right out amongst ourselves that something went terribly wrong and how is it not Oct. 31. It didn't change them, but it made it funny for us.
As for truly rude comments, I have gotten a few and mostly online. There's a multitude of those "bad cosplayer" sites etc. Again mostly it's non cosplayers, people who don't understand how much work goes into it. You can try to educate these types but you're honestly best just walking away from it, as they will cause drama and make you quite upset if you let them. Don't let them.
Part of cosplay is being asked for photo's, most of my photo's on my page were taken by other people at the cons which I have tracked down to get my photo's. I find having a card with your online alias, and places where you have your cosplay helps finding those photo's. It's really fun when you get some people together from the same series and hold a photoshoot.
As for who I cosplayed in public....It might be quicker to have a gander in my gallery. I have worn every single one of those costumes on the bus, or on a plane.....To the coffee shop, etc. xD