If I am making homemade wine-based vinegar, is there a way to tell if it's just plain soured wine? One recipe described the process as leaving the wine mixture open for a few weeks - is there a turning point: Vinegar versus bad wine?
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.
You should get a flabby-looking bacterial colony in there called mother of vinegar. That's the little guys that turn the alcohol into vinegar.
I'm not sure how easy it is for it to form spontaneously and/or to introduce it. Mine has been around for quite a while, borrowed a small piece from my parent's when I left the house. I just refill the bottle with red wine and filter as much as I need with a coffee filter to use it.