Revealing mistake: When the sniper is aiming at Swagger and the soldier through the window, a woman walks in and notices him. He shoots her and she falls. The problem is, he shoots at nothing. She simply turns her head and acts like she got hit. There's no indication a bullet even hit her.
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)