At the very end a news bulletin states "There is still no word on the disappearance of Air Force One carrying the Secretary of State ..." Air Force One is NOT an airplane, it is any Air Force plane which is carrying the President, and the designation is NEVER used for another government official like the Secretary of State even if they are on one of the planes normally used to carry the president.
In the opening gambling sequence there is heard a "phone call for" page over the casino's speaker system. No casino would allow pages like that, it would distract from people gambling. That's also why there are no windows or clocks on the gambling floor.
They got De Floria's wrong. In the original series, the agents came into the shop, walked past the cleaner and entered the dressing room on their right. Here, Solo enters and enters a dressing room on his left before getting to the cleaner.
After shooting the Armour plated door in Thrush's headquarters, Napoleon kicks the door in. As he enters, a person can be seen be seen by his feet, in the room beyond. They quickly duck out of shot.
When Solo and Kuryakin meet up in New York, they take a walk in the streets. Near the end of the sequence, after Kuryakin hits Solo, very tall palm trees can be seen in the reflection in the window.
Upon leaving Caesar's Palace, Solo gets into his car - a convertible with the top down. Markovitch pops up from the back seat surprising him. He certainly should have seen her there as he walked up to the front door, but beside that, she couldn't have possibly known which car was his.
At the end of the opening gambling sequence, the guard grabs Andrea Markovitch, slaps her, then rears back to slap her again. Solo grabs his arm and gives the guard a little slap. This must be Hollywood's way of trying to reduce violence on TV because the original Napoleon Solo would have slugged the guard with his fist.
In the final poker hand, Vaselievich is showing three kings and Solo says he has a possible full house. While true, as a true gambler Solo should have said he has a possible four-of-a-kind, since that hand is ranked higher than a full house.
Joining the chase, J.B. puts his gun down on the car seat next to him "just in case". Nobody in their right mind would do that - the gun would go flying off at the first turn or brake - but then nobody considers Hollywood writers to be in their right mind.