Continuity mistake: When they are driving up the mountain to get to her kids, they cross a river and they get hit on the passenger side of the truck shattering the window, but later when they show them going up the mountain there is a new window there.
Continuity mistake: Just after the helicopter crashes, check out the two full-view shots of the vehicle that show the top running lights. Of the three that are left, the middle one has been knocked crooked. After these two shots, the lights are all perfectly aligned again.
Continuity mistake: Near the start of the movie, during the violent eruption when the major characters have quickly loaded their gear into the truck and are trying to escape, the shot changes back and forth from looking into the cabin of the truck from the front and then looking forward out through the windscreen. The windscreen wipers are running at very different speeds. From inside, they run very fast (probably so you can see out through the mud) and very slowly from outside (probably to accentuate the mud etc).
Continuity mistake: When Harry, Rachel, and the kids drive into the mine at the end of the movie, there are already tire tracks there before them, despite plenty of ash having fallen to cover tracks made earlier. Who would have been going in or out of the mine before that?
Continuity mistake: When Harry and Rachel are making their way back to Rachel's house after the volcano's initial explosion we see them go down an alley to avoid all the traffic. As they move down the alley we see a pile of bricks fall from a roof and hit the front of the truck and window which causes large cracks in the glass on the passenger side. However, immediately after this we see the car and in all shots from the outside of the vehicle the cracks are no longer visible.
Continuity mistake: The watch of one of the councilmen shows 1.40. (the stubby one in the white shirt, the one that tries to get the investor to invest in the city). Some 18 seconds later it shows 1.45.
Continuity mistake: When they get in the boat to cross the lake, they notice dead fish floating on top of the water. On the other side of the lake, there are no dead fish.
Continuity mistake: After Terry falls in the crater, watch Harry climbing down to him. Harry is almost down, then the scene flashes to him at the top of the rim again, and he makes his way down a second time.