I have a bottle of white vinegar on which it says that the presence of deposits is normal. My problem/concern is that there are LOTS of deposits. What are they? Is there any danger associated with eating these deposits?
There are unfiltered vinegars on the market that come with a lot of solids, and it's perfectly normal for those to have all kinds of chunky weirdness if they've sat for a little while.
If your distilled vinegar gets cloudy, I'd worry. That shouldn't happen. Still, foreign bacteria do NOT grow well in vinegar. If your distilled vinegar is growing something, you probably know why.
Commercially produced vinegar very seldom goes bad, unless you're storing it outside on your deck, or something. If you brew your own, your mileage may vary.
*This is often a result of leaving live bacteria ("The Mother") in the vinegar. Some people think this makes it better, like live yoghurt cultures. There isn't much data either way, but it's certainly not harmful.