Hi,
I took the lower glovebox off when I installed my AUX-IN audio adapter. There's not a lot of hardware holding it on.
I posted some pictures in
this thread in the Audio forum. You can also see how to remove it in
Honda's audio accessories instructions.
In a nutshell, there are three things holding it on: the gas shock/armature that keeps it from opening all the way to the floor and slows the descent of the door; two stops that provide a mechanical stop on opening; and two screws at the very bottom holding the door to the car.
It's really easy to remove. You have to take a screwdriver or some other prying device to the covers on the stops, but they come off easily.
What might be wrong with yours are the bottom screws. The mounting plates on the glovebox itself have little cylindrical tabs that fit into the lower dashboard to make sure the glovebox is properly aligned. Perhaps your tabs are not in their little holes.
Either that, or the stop tabs are not properly inserted. Just remove them and put them back.
Good luck!