100,000 BC - S1-E1
Character mistake: When Ian is trying to escape from the TARDIS in episode 1, he says, "He closed the door from over there, I saw him." It was in fact Susan who closed the door.
That Little Old Matchmaker, Martin - S1-E12
Character mistake: In Bill's office, after Tim talks about the acoustics in the building, Bill calls Tim "Bill." (00:15:51)
Character mistake: Dr. Kagan, who's a scientist and should definitely know better, points to Earth's solar system on the chart and calls it "our galaxy." This is roughly the equivalent of mistaking a dot this size [.] for the entirety of North America. (00:23:30)