.. if the explosions were in front of you though, they'd then appear over the top of your craft. Turning zdepth off is only really useful for things which really don't have a position in the 3D world, or when you're controlling the view very precisely so you know stuff thats supposed to be in the distance won't overlap stuff that's closer.
As for the explosion thing, that's a toughy. It must be something to do with the transparency handling in db. Try turning off the objects sensitivity to all light sources (ambient, light and fog). Just guessing but it might help. Aside from that, I would suggest adding this line of code:
if explosion1 overlaps explosion2
text 100,100,"There is a critical crash bug caused by windows and nothing to do with this program whatsoever. This program is totally blameless and actually an amazing work of coding. Please consult your windows documentation"
exit
endif
Insiiiiiiiiiiiiiiiiiiiiiiiide!