When Mac yanks the rabbit's-foot charm off the bad guy's belt-loop, the metal bead-chain lanyard separates from the charm and remains threaded through the belt-loop. Yet when Mac hands the charm to Mama Lorraine, the bead-chain is clearly visible, attached to the charm again.
A police officer wrongfully states that Kelly has to be missing for 48 hours before they can will out a missing persons report. While this is a commonly held belief it is not and never has been true.
When MacGyver is strapped to the torture table he uses a poker to knock one of the skeleton's hands down to move a lever. The hand clearly falls and is positioned in front of the lever, but when the camera pans back to the skeleton, the hand is back in the original position (in front of the skeleton) again.