In the opening scene, Bozer and Leanna are running and come upon a locked gate. Bozer finds a hole in the fence and they both crawl through. Just a few seconds later, you can see the gate wide open in the background.
During Bozer's early classes, a bunch of books is dropped on the table. One of them has a spelling mistake in the title on the cover, "Methedology".
MacGyver is set in the same shared universe as Hawaii Five-0, per their crossover episode. William Baldwin had a story arc as crooked cop, Frank Delano, on Hawaii Five-0 a few years ago. Here, he plays a different character, Riley's absentee father, Elwood.