When MacGyver and Kelly are trapped in the freezer room, MacGyver rolls up some cardboard and sticks it in the door lock. Some subsequent shots of the door do not show any cardboard in the lock.
When Kelly serves Mac a cup of coffee with "help" written inside, the cup keeps changing from a white cup to a brown cup.
When Buddy tries to dislodge MacGyver from the tail of the plane, he turns the wheel violently left and right and several times you see MacGyver pull the rudder and the inside shot shows the wheel jerked to one side. The rudder is not controlled by the wheel it is controlled by pedals at the pilot's feet.
It would have taken far too long a time for the light bulb to melt the ice, so that it could run down the metal channel, to collect in the cardboard in the lock, and then frozen enough to rupture the lock. Also, the outside would not have been frosted unless the inside was so super cold that the outside heat was not enough to prevent it from frosting.
When Mac is put into the walk in freezer, he proceeds to push aside a side of beef which doesn't appear to be frozen. He then grabs several metal items to use in removing the door handle & making a 'water ramp'. His skin would have frozen upon touching the metal that you have to assume has been in that freezer for some amount of time.
There is only an inch or two between the sides of the armored van and the tractor trailer it is being transported in. How did the bad guys get in the van to back it out of the trailer? There is not enough room to open the doors.
During/after the final fight scene you can see wheel chocks magically appear under the wheels of the airplane.
It had previously been established that MacGyver was raised in Minnesota. In the opening monologue, MacGyver states that his father used to take him to a fishing hole named Sparrow Lake, his father's favorite. However, the airport near the lake sports an Arizona state flag, while this might have been his father's favorite fishing spot, Arizona seems a bit far from Minnesota to take a child on numerous fishing trips.
Once inside the cooler, Kelly, who should be freezing cold, doesn't think to roll down her sleeves or button her blouse up to her neck to try to keep warm.