When Mac climbs up to the window of the abandoned asylum, the windows are small-paned two-row window sashes, but when he pushes open a window, it is a tall-paned single-row sash.
Mac approaches the last window on the right as he prepares to climb in, yet there is another window on his right as he climbs in.
The angle of the sun does not match in the exterior/interior shots of Mac's houseboat when the police arrive. The first shot of them going in shows the sun at their backs and the interior of the houseboat in the dark as Mac and Lt. Murphy open the front door, yet when they go inside and find Pete tied up, the sunlight is coming in from the back windows, flooding the room and the inside front wall with light.
The water level in the bathtub is inconsistent between various camera angles.
The D.A. states the call wasn't long enough to trace. This may have been true with old mechanical telephone switches where the connections literally had to be traced from one switch to the next. With modern digital switches (in use since the early 80's). The switching computer knows the calling number, the called number and any billing information just to complete the call. Part of this information, the Caller ID number is sent to the receiving phone before the second ring.
When Zito's guards are found dead in the elevator, the sheriff says "We've sealed the building", yet moments later Zito's counsel leaves the building unchallenged and other people can also be seen freely entering and leaving the building.
When Dr Skinner's car won't start, she leaves it unlocked and with the window wound down as she leaves to take the taxi instead.
MacGyver and the two officers just stand there while Zito drives off with the doctor in a taxi. They all have vehicles to pursue in and can very quickly catch up with him, as well as calling in for road blocks. He wouldn't get far in a taxi with who knows how much gas left in the tank from driving costumers around.
Several of the mathematical clues left by Zito use entirely redundant and unnecessary parentheses. Someone of Zito's intellect would not make that error.