It would be nice if T-Mo would fess up to this issue, but they are trying to sweep it under the rug. Anyway, here's the deal...
If you open the device, hold it by the keyboard section and *carefully* position the G2 to have its screen facing the floor, it should stay open. If the hinge just flops to gravity, you have a defect. Momentum and inertia will still move the screen about, but it should be able tho hold itself open or closed without provocation. However, NONE of T-Mobile's reps seem to know this.
The first G2 I received from T-Mobile literally fell out of my hand when I pulled it out of the box because the screen unexpectedly flopped open. To make quite a long story short, I was able to get it exchanged and actually got one with a good hinge.
I ordered the G2 from customer loyalty because I was hanging by a thread as it is, but the way they are handling this is unprofessional. Even though the tracking on my original G2 return has been marked as Delivered for weeks, I'm still being charged for two G2s on my bill. They promise me that'll get fixed before the bill is due, but I am wondering what in blazes they are waiting for.
I eventually went through about a dozen stores including T-Mobile, Best Buy and Radio Shack and about half the G2s I looked at had the floppy hinges. After hearing the Android Central podcast that mentioned the HTC knew about this issue and actually fixed it before release, then thinking about how T-Mobile is handling this whole thing... I was livid.
Sorry about my inability to hide my frustration, but I'm about one straw removed from switching to Verizon on this one.

The only thing keeping me in for now is that I have a functioning G2 and this phone is admittedly pretty killer.