At the end Dr. Hedges refers to the fact that people in the future need uncontaminated genes to cure their mutations. However nobody else was present when this was explained to Victor by the future woman and neither of them ever told this to the others before dying.
The clock on the wall of the laboratory shows 2:50 numerous times, once in the evening while the main characters are out having dinner and watching a movie.
The car rented from Hertz is a 1958 Edsel. When it is seen leaving the airport, its high beams are on which means all four headlights should be lit -- however the inside headlight on the driver's side is out. The next shot shows the car with just the two outside lights on.
Professor Erling claims he didn't know the statue was radioactive after he carbon-14 dated it. However, carbon-14, in addition to being itself a radioactive isotope, would certainly reveal the presence of any existent radioactivity.
Although the narrator claims the first satellite launched by "man" was in 1958, it was actually the Soviet Union's Sputnik 1 that was first on October 4, 1957. Interestingly, the first *American* satellite, Explorer I, was indeed launched on January 31, 1958 (February 1 in GMT).
Carbon 14 testing cannot reveal future dates (a possible alternative would be to show a relatively recent artifact date impossibly old because it came from the future).
The Carbon 14 method does not work with metal objects but only on materials that were once living (or part of a living organism). In other words: the method can be applied to such materials as wood, leather and bone - but not metal or mineral.
In the scene where the two scientists to whom Dr. Hedges has sent the statue for analysis discover it is radioactive, the shadow of the boom microphone can be seen on the window blinds.