I was thinking how do you tell someone something like that without being shy about it and without embarassing the person ?  I don't think it can be done without entering an awkward situation. 

And so I say that it's the person's responsibility to check their physical appearance before going out to the public... and to constantly check.   If by unfortunate circumstances your clothes get ripped, stained or some insect is crawling on you, I'd say you should be the first to know than someone else.

It's not easy though, as I remember years back, I was rushing to work and while I was walking, a lady told me that my shirt was inverted.  I checked the tag and she was right.   It was so embarassing and I was nowhere near a place to change.  Thinking of whether to ignore my shirt and hope no one would notice it or change in public, I decided to change instead and looked for a car so I could hide beside it while inverting my shirt.  It was embarassing but I learned that no matter how late I was and hurrying that day, I should've checked my shirt. 

What's more embarassing was one time, I wore 2 entirely different shoes.  And I didn't notice it until after 20 minutes.  No wonder my feet felt uneven.  You could imagine the extreme shock on my face to find out that my left shoe was brown and my right one was black.   I didn't mind being late that day.  I knew that I had to fix my shoes or endure the embarassment the entire day.

Be responsible and avoid the embarassment.