(at around 1h 21 mins) The one-lane bridge leading out of town is wide enough to fit two cars side-by-side during the evacuation, yet when the vulcanologists are fleeing in the Humvees and USGS van later, it is barely wide enough for one vehicle. This is because this scene features a miniature bridge and model vehicles. When Paul's van is stuck on the edge of the bridge at the end of the sequence, everything is back to full-size again and you can see there would be room for two vehicles side-by-side.
Some of the buildings in the town that were destroyed by the earthquakes in the original eruption were still standing and then destroyed again when the pyroclastic cloud hit.
(at around 1h 3 mins) Harry's truck emerges from the river completely dry.
(at around 1h 3 mins) The passenger side window is destroyed when the car hits Harry's truck in the river, yet in all subsequent scenes, it's there.
(at around 8 mins) The motel clerk is wearing glasses only when shown from behind.
(at around 1h 24 mins) When Harry drives the green pick-up truck over the thinly crusted lava flow, the truck comes off the flow with nothing more than four flat tires and a charred bottom. In reality, lava is capable of temperatures as high as 2,000 degrees Fahrenheit, which would have melted the undercarriage and left them trapped.
(at around 1h 24 mins) The heat from the lava flow they drive over would have ignited the fuel in the car among other things.
(at around 1h 29 mins) In order to escape the effects of a pyroclastic flow they would have to enter much deeper into the mine.
(at around 1h 28 mins) In one of the scenes, the pick-up truck was trying to outrun the pyroclastic cloud. A pyroclastic cloud moves at up to 700 km/h (450 mph) and could not possibly be outrun by a truck with no tires.
(at around 58 mins) After the eruption (following the meeting in the school) we see many broken cables flowing around. In reality, that would have short circuited the town's electrical system and the whole town would have gone dark.
(at around 19 mins) Doctor Dalton reports that there is enough carbon dioxide coming out of the ground to kill trees and wildlife. While this is true for animals (which would suffocate), trees and other plants would thrive in heightened carbon dioxide levels. Carbon dioxide is deadly to trees and other plants in high enough amounts.
(at around 1h 10 mins) When they go to save the grandmother, just before the lava comes bursting through the wall, the grandmother has a garbage bag in her hands. When the lava breaks through, she appears to drop the bag and starts running. Then they show the whole family outside, and the bag is back in the grandmother's hands, with no time for her to have picked it up. In fact it was Mayor Wando who dropped her bag; she was standing in front of the grandmother, making it appear that she dropped hers.
(at around 30 mins) When Harry and Terry are measuring the concentration of sulfur dioxide in the caldera, the instrument probe is protruding out the open cabin door into the helicopter down wash. Sulfur dioxide is more than twice as dense as air; it may seem highly unlikely that this technique would provide any meaningful results, but the instrument that Harry and Terry are using is a Barrington Correlation Spectrometer (COSPEC), which measures SO2 concentration by comparing the difference in UV spectrum seen by the instrument to a known value. Therefore, the depicted use of the instrument is correct, and is in fact the same way volcanologists measured SO2 levels prior to the Mt. Pinatubo eruption in 1991.
(at around 56 mins) After the town hall meeting, people are running past the trophy case when the quake starts. Everything is shaking and falling except the trophies which stay perfectly still in the cabinet.
Tremors strong enough to reduce buildings to rubble hit the town, but the trees lining the sidewalk remain motionless.
(at around 1h 23 mins) When Harry and Rachel with her kids hot wire the township truck he jumps wires together to start the truck. But when he backs up the truck to try to drive over the lava while the kids are jumping into the back seat there is a key in the ignition tumbler rotated forward.
(at around 59 mins) 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.
(at around 59 mins) When part of the freeway collapses, cars on the section still standing do not move, for no reason.
The design of the robot makes no sense as it is obviously designed only to operate on level ground. The vertical orientation of the legs and the fact that the legs operate in rigid pairs makes it unsuitable for rough / steep terrain. There is no way that the USGS would have such an item.
(at around 1h 35 mins) At the end, the rescue crew removed Harry Dalton from the vehicle wreckage then pull out the wrecked vehicle and go in for the Mayor and her two children. In Harry's injured state with the bone protruding from his elbow in such a way, it would have made more sense to remove the vehicle from the entrance, then remove Harry from the wreckage and cause as little pain as possible to Harry. Not to mention the fact his colleagues throw their arms round him and he forgets to wince as if he wasn't injured.
One of the credits at the end of the movie misspelled Pierce Brosnan's name as "Mr. Bronson's Driver"
Many cars leaving the town make it look like there was 1 car for every 10 inhabitants.
(at around 12 mins) When Mayor Wando pulls up to the mine to pick up Graham, she makes a motion to beep the horn but the sound does not match up.
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.
(at around 48 mins) In the bar scene, the night before Harry and the gang are to depart Dante's Peak, Paul walks up behind Rachel and Harry and calls Rachel by her real name Linda. (in the VHS version)
(at around 1h 6 mins) After the helicopter crashes Harry urgently tells his co-worker on a walkie talkie "we have a chopper down! Send the fire services..." Under the circumstances of an ongoing volcanic eruption and widespread chaos giving this such priority makes no sense, especially considering the helicopter crashed on the outskirts of town killing everyone on board and the resulting building fire appears to be no threat to anyone (townspeople are all evacuating anyways).