Major John Cross' rank insignia is an oak leaf (correct for Major) when he is introduced. Later, while in the woods with Jaime, he is seen wearing full-bird Colonel insignia (an eagle) on the right side of his collar. Over a matter of minutes during conversations in the woods, his right collar insignia alternates back and forth between the oak leaf and the eagle.
Throughout the sequence of the John leaving Jaime alone by the campfire and her following him, the time of day changes randomly from nearly dark to late afternoon to broad brilliant daylight.
When the army guy (father of the Vietnamese girl) is talking to Jaime at the campfire, her hair changes from being loose to being tied up in a ponytail, back and forth, between the close-ups of Jaime and the long shots picturing them both from the side.
The horse-chase supposedly takes place at night, yet in a number of shots, it is clearly daytime (trees/bushes illuminated by natural-spectrum-light rather than silvery moonlight, bright sunlight on Kim's face, etc.).
The chair legs have just plain tips, but in the closeup shots of the legs being trimmed, the tips are fitted with metal bolsters.
The rope that John removes from his saddle-horn is much shorter than the one he uses to attach to a tree across the road and extend down the cliff to where Kim and Jaime are.
The chair's legs would all be the same length, so measuring them would not help; as a schoolteacher, Jaime should know enough about ordinary physics to realize that the chair's unevenness is not caused by a too-long leg (especially since the chair is obviously still quite new, with clean flat bottoms on all four of its legs, not with three of them worn down more than the fourth one), but by the chair's joints coming loose and allowing the chair to flex or warp.
Jaime would not have been allowed to have a sharp metal wood-saw on an open and easily-accessible shelf in her youngster-filled classroom, especially since most of the students had started out being emotionally disturbed and/or unruly, and so it would be especially unwise and unsafe to have anything within their reach that someone could get hurt on.
The same chair-leg is shown being trimmed twice; obviously the same footage of high-speed sawing was reused.
John does not make enough cuts in the chain-link fence for several pieces to fall off the way they do; obviously the fence was pre-cut in strategic spots before he started cutting it on-camera.
The helicopter supposedly drops John and Jaime off in the wilderness, yet the mostly-buried end of a shiny metal culvert is clearly visible among the "natural surroundings" shortly after they start out on their trek.
When Kim peeks fearfully down over the side of the ledge while she's lying on her back, we next see a "camera slowly panning over the edge" shot of what is supposed to be Kim's point of view, yet the scene also shows Kim lying face-down at the bottom of the cliff.
Jaime is an experienced OSI agent with a fairly thorough knowledge of basic survival skills, so she would surely know better than to leave a campsite with the fire still burning, especially in a dry wooded area.
Jaime has gotten the campfire burning brightly, yet she still keeps whirling the fire-starting stick for several seconds afterwards.