When Amy hides the report to the nuclear waste disposal chamber, she places it horizontally. When he returns to take it with Macgyver, it is obvious that the report is placed vertically. Apparently, he has not been there, all this time, to change the position of the report..
When Amy and MacGyver are trapped in the Nuclear Waste Disposal Chamber, Amy tells MacGyver it'll get too hot to breath in the chamber minutes before the nuclear slug fills the chamber, yet when MacGyver breaks them out and she tells him to close the door quickly, the chamber immediately starts filling with the waste. The air in the chamber never gets as hot as she says, before the sludge pours in.
The funeral for "Amy" is held at 10 a.m. the morning following the car explosion. There is no way a funeral would be held so soon after the person was "killed" in a car explosion, especially before the body is positively identified.
When trapped in the waste disposal chamber, the 'cut ins' used for the reactor are actually the cutting heads of a TBM (Tunnel Boaring Machine).
MacGyver turns the nut on the pressure relief screw clockwise, which would tighten it, not loosen it.
When MacGyver and Amy are trapped behind the time-locked door and Amy says, "With fifty-nine minutes to go. Mac, we've got nine!" her lips clearly form the shape of a different word than "nine".
MacGyver attends Amy's funeral. After the priest finishes MacGyver heads to his car and Amy is in the back seat. They drive off. Next scene MacGyver says he saw her coffin get lowered into the ground, however he left the funeral before that happened (and the coffin was still visible above ground when he drove off).