Hi tdol.

Thanks very much for helping me understand this.
I would like to ask some more additional questions but, thanks to you and other people who kindly responded to me, I feel I'm getting very close to the "right feeling" which the native English speaker has when he says "the wrong..."
This web site is the best place I have ever found where I can ask questions about English (for free!) :D

First please read my response to Francois above, in which I explained my "hypothesis" again.

This comment stuck out for me because here you are saying you'd say "the wrong person" not because it is a specific person but because "there's a specific reason why they are wong."
If I understood what you are saying here correctly, are you saying it is because there is a specific criterion according to which whether the person in question is right or wrong (i.e. whether it is her or not) is decided?

If I try to explain by my hypothesis why the indefinite article is used in this example, it is used not (just) because there are many wrong turnings -- there are many wrong numbers too -- but it is because the criterion for a right or a wrong turning was not pregiven.
Or, to put it in another way, it is not just because there are many wrong turnings but also because there are many right turnings (like there are many nice haircuts and many not-nice haircuts).
Maybe I'm putting it in a confusing way...
What I want to say is exactly what Francois said, i.e. when you would say "the right...," its counterpart is "the wrong..."; and when you would say "a right...," its counterpart is "a wrong..."
Is this off the mark?
What is the counterpart of the above example? -- "He took a right turning" or "He took the right turning"?

This way of thinking makes me construct another test case:
If you knew that there is only one right turning and you were watching him from behind, thinking whether he would take that specific right turning, can you say "He took the wrong turning"?

One more test case:
If there is a specific haircut which is "bad" for you (the bad haircut) and any other haircuts are nice for you, can you say "You have the nice haircut"?