Trivia: When Rip Hunter gets knocked over the edge of the building, he reappears standing on the Waverider (the time machine) as it rises up, with his arms crossed. He does so in the same manner as Marty McFly did in Back to the Future 2 when he reappears standing on the DeLorean (the time machine). They even used part of the Back to the Future theme music for the scene.
Trivia: Not quite a mistake given the fictitious nature of the show; but in 1960, as a college physics professor, Ray makes a comment indicating one of the guys in his class is Bill Gates' father. Bill Gates' proper name is William Henry Gates III, and the man in class would be William Henry Gates II (or William Gates Jr.), which should have been enough of a clue for Ray who this man was. However, Bill Gates' father graduated from law school in 1950 and would have been 35 in 1960, not some young college kid taking a physics class as shown.