Continuity mistake: At the end of the film, when the comet hits, the tidal wave washes over New York City, smashing first into the Statue of Liberty, then Downtown and the World Trade Centre, then sweeping uptown, depositing Lady Liberty's head somewhere in Midtown. The only problem with this is the fact that Manhattan Island doesn't face East. It doesn't even face the South. It lies on an angle in a Northeast/Southwest direction, top to bottom (1:00 to 7:00 on a clock face). That means a wave that started in the middle of the Atlantic would have to take a pretty sharp right turn at Brooklyn (over 90 degrees) to travel uptown in a North-easterly direction.
Continuity mistake: During the scene where Jenny is on the dock trying to interview Secretary Rittenhouse, the sun changes position a few times during the scene. When Jenny is talking to the little girl, the sun is behind Jenny appearing to be the middle of the afternoon. When Jenny walks to look over at the cargo, the sun is now ahead of her to the west, getting closer to sunset. When Rittenhouse appears on the boat, the sun is back to the previous position, for a second until the camera pans back to Jenny with the sun out west again. Rittenhouse ushers off his daughter & she walks off as Jenny tries to talk to him, all the while the sun is now behind Jenny to the mid afternoon setting. When Rittenhouse walks off, the camera pans around and now the sun is in the west again near sunset and remains this way until the end of the scene.
Continuity mistake: When the astronauts start drilling on the comet, they ask Spurgin Tanner how they are looking for time until the sunrise cooks them all, to which he replies "it's getting tight... 1:36:30." A few seconds later they show the display in the ship and in the bottom corner you can see "SUNRISE CLOCK 00:44:11." Moments later the camera zooms fully on the corner of the display and it shows "SUNRISE CLOCK 01:36:00".