When Mac points out the plant with the knock out drug, a green plant all by itself is shown in a close up. When Harry bends down to cut the plant it's a totally different one.
During the opening gambit, MacGyver is seen using the temperature switch to turn on the toaster oven, and the "toaster timer" switch was not pressed down. But a later shot of the toaster oven while it's melting the ice shows that the "toaster timer" switch is in the down position.
MacGyver uses a piece of bark and two reeds to fool Axminster into thinking they're still underwater. When Axminster's henchman pulls the bark out of the water, it's a different shape to that which MacGyver used.
When MacGyver is sitting on the tree branch, he leans over to begin chopping it with one hand. In the closeup shot however, he's clearly using two hands and is no longer sitting on the log.
The vegetable oil Mac uses in the opening gambit starts out as a whitish liquid while on the counter, then, on the close-up, becomes vegetable oil (light yellow color), then afterwards, when Mac uses it to coat the floor, turns back to a white colored liquid.
In the cold opener, Mac is seen picking a tumbler lock with what appears to the sewing awl part of a Swiss Army Knife. This is impossible with this type of lock.
(At about 13:40) The Greyhound bus which MacGyver arrives in and his grandfather's pickup have identical license plates.
Close-up shot of the tree limb that Mac is chopping at shows the "limb" rolling slightly back and forth as Mac chops at it, showing it's just a loose unattached log, not a solid tree branch.
Mac uses a mat to protect himself against the barbed wire on the fence while climbing over it. But he can be seen on more than one occasion holding the wire with nothing but a gloved hand and resting his weight on it.
In the opening gambit, after MacGyver switches on the toaster, he re-positions it slightly; when he moves it, the power lead and plug are visible laying on the work surface, showing it is not in fact plugged in.
Whenever Axminster talks, his lips never move, clearly giving away that his voice has been dubbed in.
Harry says they are going to a town in the "high desert" He presumably meant to say the "high country".