When Director Thorton is introduced, MacGyver calls her Mrs. Elcar. It's homage to the original director, Dana Elcar, who played Pete Thornton in the original series. Elcar's stand-in on MacGyver (1985) was Don S. Davis, who went on to co-star with original MacGyver, Richard Dean Anderson, on Stargate SG-1 (1997).
The plaster dust on the palm reader "MacGyverism" that he performs is taken from The Human Factor (1986).
In the end of the episode, we see an aerial scene of the Griffith Observatory right before the gathering in MacGyver's house. In Pilot (1985), right after the intro we see the Griffith Observatory and a scene after where MacGyver calls it "home".
MacGyver's intro voice over reveals his name as Angus MacGyver. In the original series, MacGyver (1985), MacGyver's first name was never used or revealed until the final season.
Series star Lucas Till and Guest star Vinnie Jones appear in the X-Men film series. Jones portrayed Cain Marko/Juggernaut in X-Men: The Last Stand (2006) and Till portrayed Alex Summers/Havok in X-Men: First Class (2011), X-Men: Days of Future Past (2014) and X-Men: Apocalypse (2016).