When Lily's father Charles is found injured, he's said to have both legs and right wrist broken. At the end of the film, he's waiting for the doctor, and his left wrist is bandaged while with his right hand he caresses his grandson's head.
The observatory is shown with astronomers working at lighted desks within the dome building. In reality, the heat from their bodies and extraneous light would ruin the view through the telescope, so observatories are generally operated remotely and certainly with no lights on!
The survivors of the Dallas asteroid are shown to be regrouping in Fort Worth. Dallas and Fort Worth are twin cities, and if an asteroid that large took out Dallas, Fort Worth and the rest of North Texas would be gone as well.
The comet shown in the closing scene is all wrong. The tail is shown being horizontal; however, comets' tails always point away from the sun, which would appear pointing up if observed from middle latitudes of the northern hemisphere. Furthermore, comets generally do not have an observable proper motion; they are usually too far away for that.
The Airborne lasers used against the asteroid are depicted as being mounted on regular jet fighters. In fact, this kind of weapon requires a much larger aircraft and extensive modifications to the ship's nose.
While airborne lasers can shoot down ballistic missiles, they're not powerful enough to destroy an asteroid, much less at the distance they do it on the movie, and because of their design, it's highly unlikely they could lock onto an asteroid in the first place.
In one scene, supposedly in Kansas City, Missouri, an asteroid strikes and badly damages a dam, resulting in a flood. There are no dams in Kansas City.
Dallas and Fort Worth are shown to be near mountains. There are no mountains within hundreds of miles of Dallas-Fort Worth. The cities are surrounded by forests, fields, or sprawling suburbs.