The parked school bus that is crushed by the falling church steeple has "Hurd County School District" on the side - a nod to the film's producer, Gale Anne Hurd.
The close-ups of the pyro-clastic cloud erupting were done in a car park with giant gas pumps under a volcano set, which pumped masses of dark-grey cloud 5 or 6 times per second.
After Ruth sacrificed herself at the lake and Harry carries her across the mountain, Ruth's legs are there with shoes. However, when he places her on the ground they aren't there.
Much is made of the fact that the one-lane bridge and the freeway are the only two ways in and out of Dante's Peak, and that upon the collapse of both, Harry, Rachel and the children are stranded. However only one on-ramp is ever seen to collapse, and despite a section of the freeway collapsing as well, nobody ever checks to see if the off-ramp (and most likely, an off-ramp and on-ramp on the opposite side for the other direction) is still standing and accessible. Even with the small section of freeway down, this is a clear escape route despite potentially traveling on the wrong side of the road for miles.
When the freeway collapses, all of the vehicles very obviously have no occupants. This is because all the cars are in reality scale models, which are used several times to film stunts without using CGI.