What's the best way to deal with complete strangers who come up and offer their criticism of how you are dealing with your elderly parent?

I suppose you deal with them the way you would with any armchair quarterback...smile blithely and invite them to spend a day (or better yet, a week) caring for your parent. Thank them for being so kind as to "volunteer" their time to testing out their theories. Ask them to come over and "show me how it's done." Or ask them a good time when you can drop off mom or dad for a visit. The minute you ask someone to put up or shut up, hopefully, they will shut up.
I am sure that these people think they are being helpful (I usually get this when I visit a doctor's office and they act as though this is my first time helping my mom). If advice is given kindly, I have more patience. If it isn't cold silence works well.

I've had "aquantainces" come up to me and start talking about my Mom's care, and I deal with it like I think everyone should. My response usually is, " I don't know you well enough to discuss my personal business with you." I don't tip toe around ANYBODY. COMMUNICATION IS THE KEY. If being rude is the only way to keep gossiping, busy bodies at bay, then being rude is what I will be. Now, I usually just get "looks" when I'm out having breakfast with my fiance. If they REALLY cared how you were doing, they would come over and knock on your door and ask you if they can be of any assistance to you. I live in a small town and am thinking of having a t-shirt made that states, " (my town) gossip Capitol of The Nation.

Well they never stick around long enough for me to offer to let them try their hand! I guess I worry too much about what other people think, plus I live in a small town where people talk. I have been the victim of lying before, so I know that if so and so claims that I was talking 'hateful' to my mother, it could affect my business (I'm self employed). I have to talk loudly and my mother has always seemed like she had attention deficit disorder. I have had people tell me I 'should be ashamed for talking to your mother like that'! The other day we went into a crowded doctors office and I said ' I think we should have made the appt. next week!' Mother said 'well looks like we won't get out until after lunch.' I told her that I wished she had waited until the next week.
This elderly man came by on his way out and patted her arm and gave her a pitying look and said 'poor dear, I hope you have a nice day,' and shot me a dirty look!
One stranger told me that I didn't have enough patience when I had to repeat myself three times to my mother because she either didn't believe me or wasn't listening. (Maybe four times is the magic number?)
I've been doing the cold silence treatment, but I guess I feel that I'll go somewhere in the town and they'll say, 'oh there's that nasty girl that argues with her mother'!
Maybe I could start wearing a long dark wig? ; )