During the first docking sequence, the station changes from rotating in a clock-wise fashion to counter-clockwise.
There are many places in the space station where zero gravity would cause things to float away. However, this is potentially explained around the 15 minute mark with a reference to "magnetized floors." It's also possible that other objects such as a brief case, items on a desk, and so on are also magnetized, preventing them from floating away. However, unmagnetized objects such as hair would still float freely in zero g.
The habitat module levels are at varying distance from the axis, and therefore moving at different speeds. The centrifugal gravity would be lighter the closer you are to the axis. The Earth II model was visually interesting, but a real habitat would require a constant gravity in all habitat areas, and would be better achieved by an O'Neill cylinder (like Babylon 5) or a torus (like in 2001: A Space Odyssey).
After the first D&D vote, the total number of ballots is 30 more than the total of yes (1,028) and no (924), and the percentages do not match. To achieve those percentages from 1,982 votes would require 1025 yes, 957 no.
The radio dish antenna on the axis of the station is constantly rotating with the axis of the station - making it impossible to lock on to a radio signal. A radio dish antenna always needs to be pointing in one direction to maintain a connection.
The astronaut's face-plates do not have a bottom edge, and couldn't possibly form a seal. The helmets also are held together at the bottom by a strap, and gaps are visible between the halves rendering them useless as part of a pressure-suit.
There are sections of the station that have no gravity (zero G). In those locations, nothing would hang. Frank Karger's briefcase would float, as would Lisa Karger's long hair.
Visible wires holding up the Saturn V third stage / Apollo during the orbital special effects shots.
Visible wires holding up the rotating Earth II.
Visible wires holding up the astronaut during his space-walk.
Jim Capa tells the Kargers that guns, not even toy guns, are allowed on Earth II yet the station's entertainment has a Cowboy & Indian movie with lots of gunfire and Matt Karger is permitted to have a P-38, a combat plane with machine guns, toy.