It’s not so much that I don’t think the info being told me is wrong, it’s also just that it comes across as patronizing. Like, I don’t like being told what to do by a total stranger–it’s just so condescending!
I usually hit back with a complete non sequitur and say something back that doesn’t quite make sense. Like, Think it will rain, Hows your dog, I’m driving today, etc. I get an odd look from them but it stops their advice cold.
But then, I’m a Dick.
Would it have killed you to button up your coat until you got out of sight?
If it was advice you were glad to get (“Don’t sit on that chair; the leg is broken.”), would you still think it was condescending?
As others have suggested: “Thanks!”
There was an elderly Russian lady who lived in the apartment below us when Whatsit Jr. was a baby. Invariably, no matter what the weather, she would cluck and fuss at us because “that poor child need a hat!” I would always smile and nod and say, “Have a great day!” and then go on about my business. I’m sure she thought I was a crazy person, but frankly the feeling was kind of mutual. She meant well, though.
I don’t see what the age has to do with this. I would just as soon call a nosy old stranger an “old bitty” as I would a nosy teenager a “little shit.” A simple “Sure, thanks” will suffice in most cases.
Explain that they’re wrong.
Well, okay, no. But I don’t know, if the advice was something like, “You might get cold if you don’t button up your coat” it would still annoy me. It’s perfectly true that I might start to feel cold but I’m not cold right now.
It’s not a particularly urgent problem. Like if I smoked and someone came up to me and told me to stop because it was terrible for my health. They’d be right but they’d be incredibly rude.
Anyway, I asked about old people in particular because I’ve never had a younger (or male for that matter) person try to give me unwanted advice. Plus you generally are told to respect your elders.
Sadly, “Smile!” and “Where’s your coat?!?” are equal opportunity annoyances.
Not completely, but a little piece of my soul would rip away and die. How old are you, anyway? 
Yeah, just politely blow them off.
I often go with my shoes untied because it is more comfortable, and I don’t give a crap. It isn’t a safety hazard because I pick up my feet when I walk (a good idea in any case) so I never have stumbled. Sometimes someone (not always old, but usually) point this out to me. I just say “I know”.
I don’t normally go around with my shoes untied, but your post reminded me of something that happened at the airport a few years back. I was flying by myself with Whatsit Jr. when he was about 3 months old. On the way off the plane, I had him in a baby sling on one shoulder, was hauling an infant carseat in the other arm, and had a large backpack on with our carry-on stuff in it. I was in the herd of people crowding towards the up escalator that led to the baggage claim area, when a very insistent middle-aged lady tapped me on the shoulder (!) and said expectantly, “Your shoe is untied.”
I suppose she wanted me, in the middle of this large crowd of people, to drop everything I was carrying, including my 3-month-old, and tie my shoe right that very minute.
I smiled pleasantly and said, “Oh, I had no idea. Would you like to tie it for me?” She looked at me like I was a crazy person and walked off. Whatever, lady. Don’t point out a problem if you’re not willing to help solve it!