The spacecraft keeps changing. Sometimes it is shown (in stock footage) as a typical NASA rocket of the era, other times it is a sleek winged ship, and sometimes it is a space station.
The interior hatch shown that is used to move from level to level is far too small for anyone to pass through. In fact, we never see anyone ever actually pass through one.
The spacious interior of the spaceship in no way resembles any of the various rather cramped-looking outside scenes. During space-walk scenes on the rocket, for instance, the outside of the rocket appears to be about 10 feet in diameter.
While the characters prepare to fire the rockets, exterior shots show that the rockets are already firing.
A great deal of time is spent firing off stages of the rocket, although exterior shots (usually) show a one-stage rocket.
The "dopplerscope" showing the ship's position in space is marked North, South, East, and West.
The Soviet exchange officer aboard is addressed and referred to as "Major Georgiana Bronski." The "Bronski" form is male. The proper name form for a Russian woman would be "Major Georgiana Bronskaya."
The spaceship is said to weigh 50 tons. This is far less than a standard NASA rocket of the time, or even anything comparable such as a tank.
Spacesuits used for spacewalk sequence have sleeves and cuffs tucked into boots and gloves, rather than air tight. The air tanks aren't connected to the suits.
When Katie accidentally hits the button to open the outer airlock door, the differential pressure should have sucked both her and Captain Mason out the hatch, instead of letting them float inside while their bodies suffered no greater injury than passenger nosebleed on a first-generation airliner. To say nothing of the fact that no airlock system, even during Project Apollo, would be that easy to open by accident.
Keep your eye on the clock that records the elapsed time following blast off, you'll note that it goes 2:58, 2:59, and then 2:60 instead of 3:00.
As the earth explodes the string holding the model planet is visible.
While Danny is floating around space the strings holding him up are visible.