I had the same problem with my 2003. It started to pop open with the least provocation within days of delivery. Take it to your dealer and they will replace it. Don't waste your time trying to fix it yourself.

 

With only a few weeks of ownership, I can sincerely say that my MINI overall has the feel of a quality-built vehicle, except for the glove compartment. Whenever I close it, the clicking noise just sounds cheap. I hope it will not have the problem in the future.