Fence + Suitcase + Americium-241 - S3-E12
Revealing mistake: When MacGyver cuts the green wire under the bomb, the wire is not tied up at both ends. (00:25:45)
Seeds + Permafrost + Feather - S3-E17
Factual error: Bozer and for that matter I would assume all of the team went to a spycraft academy. A basic subject in any of such academies is surveillance, including proper techniques to follow and stake out someone. Bozer being so inept at tracking MacGyver's father is inconceivable given their training.