On syntax, in cases like these it can be tricky to surmise whether the opening adjective should apply to the first noun or to the following adjectival noun–noun pair. Some may be clarified by means of a judiciously-placed hyphen, but that would spoil the fun:

• Vibrated concrete manufacturer
• Missing intelligence officer
• Edible oil merchants—and indeed Crude oil merchants
• Used car dealer
• Small business adviser [peering over desk]
• Great Queen Street
• Hot bread shop
• Swiss watch maker
• Fat free yogurt
• Overweight lorry driver
• Affordable housing shortage [one for conservative governments, confident that we—or rather they—can indeed afford a housing shortage]
• Wild goose chase [man, that was one wild goose chase]
• Rare book librarian [don’t see many of them around]
• Illegal migration bill [that’s just what the migration bill is],

as well as this literary contribution:

• Are you a Moby-dickhead?

and the classic

• Fine tooth comb,

and perhaps even

• One trick pony [How many trick ponies?].

A letter to the leader of a quartet belongs in this category too.

Recent news items have featured

• Huge face database
• Infectious disease expert
• Racist dog whistling, perhaps owned by
• Rightwing beer magnate:

Welcome to our theme café, Sir and Madam, I’m Fido, your racist dog waiter for this evening, and I’ll be whistling your favourite racist ditties for you to sing along to—specials on the board, and a fine selection of craft rightwing beers. (Did you just see that Pekinese? I dunno, they come over ‘ere… Woof! LOL—What am I like?) Perhaps I can warm you up by warbling The Stammering Coon.

This almost leads us towards silly headlines (rounded up here):

• Squad Helps Dog Bite Victim
• Prostitutes Appeal To Pope
• British Left Waffles On Falklands

And this, from Terry Jones and Michael Palin, no less:

Some punctuation might help here:

And a related case, under “Document design matters” on Twitter:

See also Punctuation for truck drivers, and Publicity.