I have a 2010 Trek 1.1 that I got new, at a discount and to use as my commuter, about 7 months ago.

When I test rode it, I felt and heard a slight headset clunking when braking hard. Figured it was no big deal, told them to fix it, and bought the bike. Everything seemed fine for a while, but the clunking came back. After failing to get rid of it on my own, took it back in (a few weeks into owning it).

It was inspected, and they didn't see anything wrong with it or the fork. They couldn't replicate it in the shop (it only happened when braking with pretty significant load), but made sure all the usual suspects (including brakes) were tightened correctly and put some kind of spacer in it.

Eventually it came back, and got more frequent. They replaced the headset under warranty, but it's about the same. Now it's either too tight and catching or loose and popping like crazy when I brake. Even when adjusted as perfectly as possible, something is off.

I thought the headset was probably just not installed correctly at the factory, and that a fresh installation would take care of it. It didn't. The shop has been cool about it so far. Since it's got a new headset, though, and everything is basically the same, this is probably some other issue, right? Like a fork or steerer tube issue? If it's something big, I definitely want it to be fixed under warranty.

Additionally, is it actually dangerous to ride with the headset slightly loose (knocking while braking)? They've told me I could ride around on it while the parts were coming in and such.

First double check that the problem is in the headset/steerer area as follows.

Apply the front brake to lock the front wheel, then hold the lower bearing area and even the crown while rocking the bike back and forth feeling for any movement. If you feel movement, then it's either a headset adjustment, or possibly a cup is loose in the frame or the crown race is loose on the fork. Sometimes integrated headset bearings don't seat perfectly and are able to shift a bit when braking.

If you can't feel anything, it's possible that the problem is in the brake itself or the rim joint is imperfect causing the knocking.

Lastly, I don't know how bad it is, but if not too sloppy it's OK to ride it as is for a while. It's less than perfect, so no 50mph downhills through mountain passes, but otherwise don't sweat. After all you've been riding it that for a while already.