Adolf Hitler is portrayed as a young man at the time of his death, the actor playing him was 28, but he was 56 at the time he committed suicide.
The aliens are shown to have silver skin. However, at one point when Ott raises his left hand, the actor's skin tone is visible where the silver paint was not applied.
The star Canopus is described as being 98 light years away from Earth. In reality, Canopus is 310 light years away from Earth. Traveling 98 light years would get you to Kappa Delphini. However, most of this was not known in 1967.
On at least two time the Curator corrects Tony when he talks about "sunlight", to which the Curator says the get it the Canopian sun, not the Earth's sun. It makes no sense for him to always assume that when Tony says "sunlight" he is always referring to Earth's sun (Sol) instead of the Canopian sun.
Doug asks Ann if the Time Tunnel had a fix on them when she was captured. But in the immediately preceding scene General Kirk told them directly that the Tunnel had a fix and was preparing to transfer all three of them.
Ann says the guard in The Time Tunnel was killed by the alien Ott - but in fact he was only injured and taken to the infirmary - she witnessed that. Even if he died there later (not mentioned or shown), she had been kidnapped by then and had been incommunicado with The Time Tunnel ever since and so had no way of knowing that if so.
Both the Curator and Tony agree that plants get their nourishment from the sun. This is wrong, as sunlight provides the energy plants use to remove carbon from the carbon dioxide in the air. They also ignored the fact that the roots get "nourishment" from the soil.