Yeah, dish soap works ok, particularly on glass bottles, but some label adhesive is the very devil to get off plastic bottles -- which is most of what I use, since so far, I haven't been making large quantities of anything. When I finally get done with my WTA-withdrawal and can make larger quantities, I'll be using more glass.
Don't have mineral spirits, but the ol man probably has some WD40 in the garage -- not sure I'd want to try that on plastic, the smell might linger.
Actually one of the best things I've tried for the stubborn dried on remnants of paper and adhesive is one of those white silicone erasers; it "peels" the stuff up, so you can brush away the "crumbs". Regular rubber erasers don't work as well; they tend to disintegrate rather than having any effect on the dried-on adhesive.
Andria