Continuity: After the two main characters sled down the mountain in that boat, they all fall into the river.  In the next shot, they come up from underwater, and the boat miraculously is right-side-up with no water in it.

Revealing: In several scenes (e.g. in the deli & in the tunnel, at the end) the ice cubes used to cool Elvis down are obviously not real ice.

Continuity: While directors certainly take their liberties with the military, is it reasonable to think that the security would be so lax at a government NBC (nuclear, biological, chemical) research laboratory that you could just kill two guards and walk in and open a cabinet and "hey, there's that super-secret, super-volatile weapon we've been looking for."  The military takes their security far more seriously than Hollywood interprets it.

Factual error: Chill Factor takes place in Montana, at one point the characters argue over whether to go towards Billings or Missoula. Anyone who knows anything about the southwest U.S can see that most of the movie is filmed in or around Monument Valley. Monument Valley is spread across parts of northeast Arizona and southeast Utah.

Other: In the scene where Cuba and Skeet are "negotiating" with the federal agent at the end of the movie, Cuba interrupts Skeet by saying, "I'll handle it from here sweetdick." Notice that Skeet almost breaks character due to an apparent ad-lib by Cuba.

Continuity: During the chase scene on the winding mountain road, the door on the yellow ice cream truck is wide open during the whole chase, except when we see the truck from an aerial view, then we notice that the door is not only closed but locked as well.