When Smith and the Robot go back in time, Smith is dressed in uniform he wore back on Earth, and Robot performed just as he had before launch of the Jupiter 2, but when Will went back in time, he wasn't wearing his silver "foil" jumpsuit he wore on take off. Instead he was wearing what he had on when on the planet in 'current' time.
With the alarm sounding at the launch pad, when the guards run past the robot, he is shown hidden behind a blue sheet. In the next camera shot close-up, the robot is covered with a black sheet & a blue sheet.
The deputy MP is wearing the stripes of an E-2 grade and he is addressed as "Corporal". The two-stripe grade insignia of Corporal was made obsolete in 1952. In the late 1990s, he would be Airman First Class. The three-stripe grade is correct as "Sergeant" for this time period.
Both Dr. Smith (Colonel Smith) and General Squires are in the Air Force, yet the two guards' helmets and arm bands read "MP," an Army designation. As their ranks on their sleeves are clearly Air Force ranks, the guards should have been designated as "SP" (Security Policemen).
Automotive style bulbs and sockets can be seen through the Time Merchant's transparent dome shaped "controller".
John Robinson, the Robot and Dr. Smith follow the Time Merchant back to his factory even though Will had deactivated the apparatus that brought the Time Merchant to the cave.
When Smith is transported back, the person in the cage is not Smith. It's a man wearing an obvious Smith mask from a previous episode.