Just for anyone that pulls this up later, I was able to fix the latch today. First I had to give the latch a fairly good smack from the outside to get it back into the closed, flat, position. Once it snapped into place, I was able to open the glove box. I could then see that the problem was that the two screws that hold the latch together were very loose. I tighten them, and the whole thing works fine now. I am going to pull them out and put a bit of blue loctite on them once it is above zero outside.

__________________
2002 e53 X5 4.6is Estroil blue/ Black interior (Build Date 04/02)