When Dodge and Penny go to Olivia's parents' house, Penny breaks the window. They then enter the house, and you can see the window in the background, unbroken. Then a few seconds later, another shot occurs and the window is broken again.
When a policeman is driving Dodge and Linda to Speck's house, there is a security net between the front and back seats in the police car, but after they get out, the net is missing.
When Penny and Dodge are sitting at the table in Olivia's house, Penny's arm changes position inconsistently between shots.
When they are eating at Olivia's parents' house, the position of Dodge's fork changes position.
Dodge's cleaning lady is at his home on the day the asteroid is going to hit. She says it's a Thursday, and yet the news announcer tells everyone to set their clocks forward that night for Daylight Saving Time - which always happens on a Saturday night/Sunday morning.
In the last scene of the movie where Dodge and Penny are in bed. You hear the sound of the meteor impact, which after a minute or so has the shock wave hit. If the meteor is as large as they say, the shock wave would arrive first obliterating the house before the sound would have ever reached them.
In the scene where Dodge is watching the Cessna fly away you see the Navigational lights green on the right red on the left. Those lights are never seen when an aircraft is flying away but towards the observer.
Dodge pulls out the vinyl album "Scott", Scott Walker's first solo album. He takes record out of sleeve puts it on turntable but "The Sun Ain't Gonna Shine Anymore" plays. This was by The Walker Brothers and was not on the album in question. Additionally, the following song that plays "Stay With Me Baby" does not appear on the album "Scott." Nor does it appear on the album "The Sun Ain't Gonna Shine Anymore." The two tracks only appear together on later released compilation albums.
Coincidentally though, the first track on the album "Scott" (the one shown but not played) is "Mathilde" - an alternate spelling of Matilda - which is the name of the asteroid in the movie.
When Dodge is driving the truck, the gear shift is still in Park.
Dodge grabs the dog from his apartment during the riot and carries him down the fire escape, when they flee Penny's apartment the dog is on a leash.
When Dodge is listening to the LP record and the power goes out you can hear the audio as the record slows down. The audio should have gone off immediately with the small receiver shown.
There are no ocean beaches at the base of cliffs, like the one Penny and Dodge visit, in the New Jersey / Delaware region.
The movie is supposed to be set on the east coast of the US but it is clearly being shot in California.
Speck has several Smart Cars for his fleet for use after the post-apocalyptic world. However, these vehicles are parked above ground, in the open, outside his shelter and Speck should know that all these vehicles would be incinerated by the effects of the meteor.