Yes I am having this issue as well. I am going to try the electrical tape trick that someone else posted.

 

I am surprised to not see more gripes about this. The two droids i have would easily open in my pocket from day 1. It was very annoying to pull it out and see the screen on and often have the message of too many failed lockscreen gestures or "that is not an emergency number" as the emergency dialer was up trying to dial numbers erroneously..

 

Maybe there is a screw or something that you can tighten.

 

http://androidforums.com/motorola-droid/24379-screen-loose-you-might-wanna-try.html

I did this fix because of the 'give' between the screen and the keyboard (you could feel a gap when pushing down on the screen.) It did add a bit of friction to the sliding process though, and might help for you. You could try putting just one strip (make sure it's good quality 3m electrical) along the back of the screen to add a little resistance.

 

I totally agree, have you tried exchanging it through verizon?

 

I got a replacement for my Droid a few weeks ago because of an unrelated issue. While my first one was fairly loose and would open in my pocket, the new one doesn't. It feels much different as far as the slider goes. There is just some variation among the Droids out there right now.

If you can come up with a reason to swap it, you might be able to get one with a better hinge.

 

I just got mine swapped out this morning because of the loose screen clicking issue. The new unit week 45 is much tighter and I'm pretty happy.

 

There's a thread, something to the effect of "customize the back of your droid's screen." Basically they make a vinyl sticker cut to fit the back of the screen that should add some resistance, might be worth a shot. They offer a bunch of different colors and patterns