I have the same problem.
I fall through the floor, the 'Kill all spiders' objective appears on screen. I kill the freaks until none are left, but the 'objective complete' notification is not given, and the bigass door that is supposed to open, does not open.
Can't cheat my way out of it too, because I have to tilde key.
Oh joy.
EDIT: A way to solve this problem is if someone would be so kind as to send me a savegame with the checkpoint closest after the whole spider shootout. Anyone?