In the Spring of 1951, when George and Natividad see Rita in the club, she is obviously pregnant. However, Rita Hayworth's last child, daughter Princess Yasmin Khan was born December 28, 1949, from her third husband, Prince Aly Khan.
The elevators in the hotel lobby have LED displays above the doors (to show the floor number). These were not developed commercially until the mid-1960s and did not become common until well after that.
The Los Angeles police cars seen at the beginning of the movie
outside Reeves' house are from the time period, however the red rotating warning light on the roof is inconsistent with LAPD use at the time. The LAPD cars had the two barrel lights with a siren mounted in between them on the roof. This type of warning system was used until at least the late 1970s early 1980s.
When Simo buys the newspaper from the stand, there is a red Corvette parked in front of it carrying chrome 5-spoke Cragar rims. The earliest street rim Cragar produced that looked like this, the Cragar S/S, was not released to the public until 1964.
When the child points the gun at George Reeves to see if the bullet will bounce off of him, you can hear the hammer being cocked back and the hand motion of the child also indicates he is cocking the gun. However, the gun is shown from then on with the hammer in the forward position.
During on-the-set scene of George Reeves "flying" during filming of Adventures of Superman, background music is playing on set. Except for playback on musical numbers, there would no need for canned music on set as it would be added later.
In 1958 it shows George Reeves burning his Superman costume after he hears the show was canceled. But in reality Adventures of Superman was never canceled when George Reeves was alive. It was renewed for a 7th season. The show was obviously canceled after Reeves' death.
When Louis Simo is entering the Mannix house behind the flower delivery man, the flowers' ribbons read, "Eddie and Toni, Happy Anniversary." Their anniversary was on May 31, George died on June 16. In that scene, Toni was grieving George's death. Unless they were celebrating their anniversary two weeks late (unlikely), this is an error.
In the middle of the movie when the intro to Adventures of Superman is shown on a television, the "faster than a speeding locomotive" is the wrong train, pulled by a New Haven locomotive, not the Southern Pacific "Daylight" steam locomotive seen in the series. That entire intro was not original.
Suspicious that her son is actually a murder victim instead of a suicide, Reeves' mother takes a train from Illinois to California and somehow manages to arrive in Los Angeles and consult a private eye before news of the tragedy is even announced in newspaper headlines.
When Simo drives his son to school and presents him with the gift of the etch-a-sketch, his Chevrolet's steering wheel is clearly is never correctly in the center position although he shown to be driving straight. This suggests the car is being towed on a trailer while being filmed.