In the establishing shot of the grandmother's cabin, we hear a chorus of peeping in the sound effects mix. These are small frogs often called "spring peepers" and they will usually only sing after sunset, not in the middle of the day as depicted here.
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.
The helicopter crashes into the ground nose-down and continues moving for several feet after impact, which should indicate that the cabin is being crushed; we also see parts flying off the rotor. But a moment later, it rises again in a manner completely unlike the way the wreckage might bounce, more the way it would if was still under power; and we see that the cabin is still intact.
After Harry, the Mayor and her kids drive into the mining tunnel to escape the eruption, they walk deeper into the tunnel to the kids hideout. When Harry goes back to the truck there's a collapse blocking several feet of tunnel between Harry and the Mayor and kids. During the rescue Harry comes out, they pull the truck out and then a couple minutes later the Mayor and kids come out without the tunnel collapse being cleared.
When the crew is unloading SpiderLegs in the parking lot, Greg has a highly noticeable case of five o'clock shadow. Less than a minute later, when he is inside directing SpiderLegs remotely, he is clean-shaven.
A station wagon is clipped by a black Chrysler while trying to enter the freeway on-ramp. When the on-ramp collapses, several vehicles behind or beside the wagon are seen further ahead, and the wagon has disappeared. Despite all of the vehicles forcing their way forward, there is no way that the wagon could have been overtaken by all of them (and thus the wagon "disappearing" from shot), as it is originally seen right at the beginning of the on-ramp, level with the guardrail, and the later shot featuring the other vehicles that had been far behind it, is taken from almost the same angle, showing the same spot where it had been, and there is no way it could have pulled off out of frame or reversed out of the way, due to the traffic around it.
When the volcano had started erupting, Harry and Rachel rushed back to her place in his truck to get her kids. The both of them run into her house and she found the letter from the kids. They run back out to the truck and the truck's headlights are on. They're standard headlights, which appear yellow in color. They leave and find the bridge is jammed with traffic and Harry decides to cross the river. In the shot of them crossing the road and going down the bank towards the river, not only are all the truck's lights on - not just the headlights - but they're very bright, white, possibly HID headlights until the truck's demise.
A far-away shot of the freeway on-ramp, moments before its collapse, shows the blue pick-up being struck again by the white pick-up and black Chrysler, when this has already occurred several shots earlier in close-up.
When they arrive in town after rescuing the dog, just before the big blast, they stop and Harry puts the truck into Park. The next scene he shifts from Drive to Reverse and begins to back up, but the truck was in Park.
In all the shots of the volcano leading up to the pyroclastic eruption the sky appears overcast. Then in the shot of the initial explosion the sky is shown to be partly cloudy with plenty of blue patches, although then in all the subsequent shots it is overcast again.
At the evacuation meeting in the high school, the camera starts on the crowd of residents before panning around to Harry and Rachel on the stage. During this pan, Les Worrell and Elliot Blair can be seen at the front of the crowd on the extreme right of screen. From a distance, Elliot clearly makes his impassioned "getting out" statement to Les, then turns to leave, with Les unhappily following. Note that Dr. Jane Fox, standing behind Harry and Rachel, notices this and points it out to her colleague next to her. After a few moments, it then cuts to a close-up of Elliot delivering the same line to Les, before turning to leave with the councilman in tow.
The red van that Paul is driving onto the bridge when they are evacuating the town has no vent windows, yet when Paul is stuck on the bridge, and it begins to overturn, the same van that he was driving can be seen to have vent windows.
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.
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 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.
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. He means sulfur dioxide, which is toxic to both plants and animals and would account for the increased acidity in the water. Carbon Dioxide is deadly to trees and other plants in high enough amounts.
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.
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.
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.
Numerous civilian vehicles are seen repeatedly during the evacuation sequence in multiple locations throughout the town. Most obvious are the Oldsmobile Cutlass Cruiser station wagon, white Mercury Capri, red Ford Tempo, white Chevrolet Cavalier, and tan Mazda GLC, all of which appear when there are collisions, etc. The Oldsmobile wagon, for example, has a telegraph pole fall on it in front of Harry and Rachel, then appears at the freeway on-ramp to be struck by another car, then reappears in front of Harry and Rachel again as they approach the bridge. The Mercury Capri is seen no less than five times in the same sequence (outside the high school, on the freeway on-ramp, and is the same car sideswiped by Harry on the bridge). It is extremely unlikely that several identical vehicles would be present in such a small town, and note that damage from earlier action scenes is present on these vehicles in later shots where they turn up elsewhere.