When Pete is electrocuted and falls backward, they show him laying on the ground with a brown pillow under his head. That pillow wasn't placed under his head until Karen did so when she and MacGyver came back into the room a few scenes later.
The bottle of vinegar is about 4/5 full when Mac takes it out of the cupboard and sets it on the table, but when he and Karen leave the kitchen, the bottle is full again.
When MacGyver first approaches the breaker box, the red handle is in the up position. Later after he finishes running wires all over the place, he goes back to the breaker box and the handle is in the down position. He then says "this must be his power" and pushes the handle up. That would be turning the power back on, not shutting it off (as he was intending to do).
Pete tells a story about a camel and says it's part of how he met MacGyver. Partners (1987) uses flashbacks to tell a completely different version of how they met.
When Quayle leaves his room to confront MacGyver after the power is shut down by MacGyver, he walks through a corridor well lit by lights.
Mac would not have been able to open the door to the breaker-box without first shutting off the box's main switch, since this type of electrical mains box is built with an interlock on the door to prevent the box from being opened and exposing the dangerous live-voltage connections without first shutting off the electricity to the box.
When Karen looks in on MacGyver in the kitchen through the painting, they appear to be on the same level. Yet she then descends stairs from that level. It would be rare for the kitchen to be on the second level and even rarer for the second level to be at ground level at the rear, presumably where the kitchen is.
MacGyver wonders if the front door is electrified. Incredibly, he touches the metal door with the tip of his pocket knife and says that it isn't electrified, which is a good thing, since touching an electrified door with a metal pocketknife would have been fatal for him. However, many Swiss Army knives have a plastic casing rather than metal; plastic would act as an insulator.