The original post did question what happened to the momentum during
transport. The characters did fall to the floor, implying that some
momentum was still there. But I interpreted it as being the fall due to the
materialization over the floor. It is wonderful how they can always
materialize the people contacting the floor. One would think they might
miss by an fraction of a cm or more. So why were the characters
materialized in the middle of the air in this case?
Of course nobody seems to notice that the planet is revolving and the
Enterprise is moving, so there is a relative change in velocity which might
actually be bigger than the velocity of the falling characters. So if they
can handle the sideways momentum change, why not the vertical momentum
change? I guess they have good inertial dampers in the transporters.
And it always seemed ludicrous that the captain's chair did not have seat
belts. He is always getting thrown out. But I guess the Enterprise never
went at "ludicrous" speed, so they didn't need seat belts.
It is entertainment after all. It is sometimes difficult to watch certain
old movies and take them seriously, but people did. In Flash Gordon why did
the exhaust always go out and then angle upward? Apparently most people did
not notice it. I wonder what people 50 years from now will think of Star
Wars and Startrek. Old SF tend to seems to become dated faster compared to
old dramas. One can generally accept the fact that society was different
then. The Day the Earth Stood Still is one SF that does not seem as dated
because they assumed a technology so advanced that they did not have to show
it. It still seems futuristic as long as you ignore the wrinkles in Gort's
knees.
And or course why do the detectives always violate the first rule "Call for
backup." When in a potentially dangerous situation. But the first rule of
entertainment "Make it entertaining!" trumps any real life rules.