I found a nifty explanation (written for scientists and engineers) of the proper use of the restrictive versus the non-restrictive clause. It uses (naturally) set theory.

The confusion between "that" and "which" is very common, even among professional writers and journalists, and many otherwise superlative bloggers (I'm looking at you, Mr. Den Beste...). Read it, and improve your writing almost instantly.

This really isn't a nitpick, like dangling participles and split infinitives. The words really do mean different things, and wrong usage actually changes the meaning of the sentence, though it's usually possible to figure out what the writer meant. The author of the link above has another page in which she explains why it's so important.

Anyway, the use of "which" for "that" is always jarring to my eyes, particularly because I generally expect the former to be accompanied by a comma, and it never is when used incorrectly.

Much ado about nothing??? Using the examples given I would merely say, "Tiffany likes expensive shoes" and do away with the word "that" and the subset entirely. However, "Tiffany likes emeralds, which are expensive." is acceptable.

Just think of the word "which" as being used in a parenthetical sense and all will be well.

Good points. One thing that really drives me crazy is when people misuse the term "begs the question". Of course so many people misuse it, it has almost become the only usage of that phrase.

Other pet peeves...

People that say/write "towards", what's with the "s"?
Also, afterwards. You get the point I'm sure.

Shouldn't that be "People who say/write..."?

Don,
You're right. Quoting from E.B. White:

"A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary part."

Even scientists and engineers should be able to understand that one.