During the final chase scene, Callahan and the bad guy are running down a wharf. In one view, Callahan is running through a column of steam. in the next cut, he is well beyond the steam, and the bad guy is running through it. Yet again, in the next cut, Callahan is exiting the column of steam.
The first car bomb with the remote control toy leaves no trace of its victim, yet when the next car bomb detonates under Callahan and his partner's vehicle, they are able to walk away with minor injuries, in lieu of the fact that they pulled forward a few feet before the bomb exploded.
In the final scene between Callahan and Rook, Callahan walks towards Rook holding a harpoon gun with a spool of rope, easily 25 feet in length, around his left arm. The next scene is a closeup of the harpoon gun, being aimed, but the rope is no longer on his arm. The next scene is of Callahan with the rope back around his arm. And then again a closeup of the harpoon gun with the rope off his arm.
Liam Neesons character has a pony tail - a little hair extension clipped to his real hair. After the funeral scene, Peter Swan (Neeson) is walking towards the camera with Harry and turns his back to the camera. He has a small amount of his hair in a pony tail without the hair extension. In the next shot with a side profile, he has his pony tail extension back in place.
When Harry and Al are investigating the death of Johnny Squares in his trailer, Squares has a rubber strap around his left bicep. A moment later as Callahan lifts his arm to describe the tract marks on his arms, the strap is gone.
After the killer attacks the cameraman in the garage, he gets in the news van and holds up a bloody knife to Samantha. In the next scene when they are in the shipyard building and he holds the same knife up to Samantha's throat, there is no blood on the knife.
During the opening scene when Harry is ambushed in his car he's shot at by all the people, wrecks the car, then he gets out and kills them all. The next scene shows a tow truck pulling away Harry's car, and you can see bullet holes through the driver side door and driver side rear door in reality if this happened (even with low calibre ammo, which was apparent they were not because of the weapons used) bullets will easily penetrate car doors most times go through one side and out the other (if not hitting what's inside first, i.e. like a person) so if the car were shot where the bullet holes were at, Harry would have surely been killed.
Callahan and Quan as members of the San Francisco Police Dept. are being chased through the streets by a madman with a radio controlled car bomb, and they don't radio for help? They don't call for backup, relay their position, they don't have portable police radios or even use the supposed police radio in their car. The SFPD would have been all over that chase long before it ended.
The goof items below may give away important plot points.
When Callahan leaves the killer's apartment, he takes Capt. Donnelly's car to where the killer is holding the news reporter. After Callahan finishes off the killer with a harpoon gun, Capt. Donnelly drives up in the car Callahan took.
Near the end of the movie, as the killer is walking towards where he will eventually die, we see him walking away from the camera with a bright light behind him and his shadow on the ground in front of him. To the right of this, the shadows of the camera man and other crew members are visible on the ground.
The C4 explosive composition the killer used typically came in 1.25 lb. blocks and measured 1" x 2" x 10". Although malleable to nearly any desired size, the radio controlled car used by the killer was an RC-10 radio controlled model of the 1963 Corvette, and it does not have any room inside of it to carry enough C4 to destroy a car, let alone kill anyone.