After they put the spacesuits on, Bill and Nardole go down a corridor as the Doctor looks through the door at the approaching space zombies, but immediately afterwards the Doctor is in front of Bill and Nardole as they continue down the corridor.
In the beginning scene, two dead crew members land behind the live female crew member. However, there is nowhere they could have landed FROM, since there's nothing above to drop down from. This cannot be explained by the two dead crew members seen a moment earlier, as they were tumbling in a parallel direction to the station's roof, and the two who landed dropped straight down without tumbling.
The suits are instructed to kill the crew (and a replacement crew is dispatched) due to a lack of operational efficiency while they are repairing the station's ore conveyors. The entire premise is pointless, because killing the original crew will make equipment repairs take longer, and the replacement crew would likewise be killed for a lack of efficiency while they tried to make the repairs themselves.
The Doctor explains to Bill that they need to wear helmets outside the station because of the vacuum of space. This ignores the fact that the INSIDE of the station is ALSO a vacuum, as the station automatically vents any internal air.
Since everyone in the station's crew is ON the station, there is no way there could be two crew members' bodies tumbling through space headed TOWARDS the station.
If the Doctor was paraphrasing 'the world is your oyster' when he tells the survivors that 'the universe is your crustacean", he should have said "the universe is your mollusc".
During the hazy spacewalk escape scene Bill is briefly seen to be suffering from vacuum exposure, including what looks like frost on her face. When she wakes up, however, she's totally unharmed.