There is not really a turning point. The way that wine goes bad is the process of making vinegar. From wikipedia:
The word "vinegar" derives from the Old French vin aigre, meaning "sour wine".
The Canadian government limits things that can be sold as 'vinegar' to something with an acetic acid content of 4-12%, so you could do the technical-bureaucratic thing and wait for the acetic acid to get up to 4%.
If you aren't hung up on technicalities, then you can use it as soon as it gets sour enough. It is done when all the alcohol has been changed to acetic acid, but it is a bit hard to taste since the acetic flavor dominates.
Rice wine vinegar and rice vinegar are the same thing, so that's easy.
For additional pantry-stocking:
Seasoned rice vinegar is just rice vinegar with a little salt & sugar added. It's intended to be the right mixture for a number of recipes, not the least of which is sushi rice, although in my experience you're better off seasoning plain rice vinegar to the correct balance.
Rice wine is, of course, sake. Generally if you're cooking with rice wine you want a moderately priced, clear filtered sake like Gekkeikan. The same advice about cooking with regular wine applies here; don't try to cook with anything undrinkable.
Mirin is a specific kind of light, sweet rice wine used in braised dishes, dipping sauces, steamed fish, etc. If you can't find it, buy a drinkable sake and add around two teaspoons of sugar per 1/4 cup of sake.
Best Answer
As Blessed Geek indicates, vinegar is made by fermentation of ethanol by "mother of vinegar", a bacterial culture. This is true of all vinegar, not just wine vinegar. The unique flavor profile of various vinegars is the result of other flavors in the base wine or spirit used to produce the vinegar. (Well, some vinegars like true traditionally produced balsamic vinegar get flavor from the casks in which they are produced and aged, but that is a special case.)
Finding definitive and credible sources on the amount of remaining alcohol in the final product after fermentation is difficult. One of the more credible sites indicates no more than about 2% alcohol content remains; other sources seem to indicate about 0.5%.
Unless you are concerned about the laws of Islam, or the possible affect on a recovering alcoholic, this is trace alcohol almost certainly negligible. I am not qualified to comment on what it might mean for those two areas of concern, though.