The door will move, just not open or close. The problem is that the door has a slightly upward motion when moving up and it hits the bottom of the stereo. So you either have the ashtray door open all the time, or closed all the time. Those are your two choices. The other choice you have is to completely re-engineer the door so that it folds down in case you wanted to put something in the ashtray or access the lighter socket. Probably wouldn't be too hard for a crafty installer to do this either.
I solved this but it took a bit of work:
A picture of the install.
Ash tray door closed....
Ash tray door open.
Shaved about 1/8" off the top bracket of the SOS mount (so I could mount the IVA-W200 as high as possible without hitting the CCU.) Shaved the bottom of the CCU so the stereo wouldn't push it up. Also shaved the ash tray door cover to half of it's original thickness and beveled the top edge (after peeling the electro-plating off of course). Removed about 1/8" off the top of the ash tray door (the black part the cover screws to) and had to shorten the black metal housing that goes around the back of the ash tray assembly by about 3/16". Then I had to elongate the mounting holes for the ashtray so I could mount it just a little lower on the back of the center console. The ash tray door still barely touches the bottom of the IVA-W200 when you open it but I put some felt tape on the bottom of the Alpine so the ash tray cover won't get scratched.
Here's a link to the entire install for those that are interested...
http://www.nsxprime.com/forums/showthread.php?t=104260