Continuity mistake: From the Mars rocket's cockpit, Boomer hears Thomas scream once, shouts, "I'm coming!" and races out. When Earth Command hears this on delayed radio transmission 3.5 minutes later (it would take much longer than that from Mars, by the way), there's added dialogue, and this time Boomer never says "I'm coming." We also hear Thomas scream twice instead of just once.
Deliberate mistake: Though by 1964 it was already suspected (and later confirmed by Mariner IV) that Mars has an atmosphere humans can't breathe and temperatures too low for humans to tolerate, Merritt and his crew are here exploring the planet sans spacesuits. This was "fudged" because space helmets A)are expensive, B)reflect cameras, and most importantly, C)obscure the actors' faces.