The red marks on T'Pol's face and upper chest appear and disappear between shots. Moreover, if they are bruise, rashes or other lesions, they should be green, on a Vulcan.
When trying to escape the asteroid in the shuttle pod it is stated that they are having trouble with one of the thrusters because an intake manifold is jammed with debris. Thrusters are like rockets, they have contained fuel sources, they do not intake air like a jet, and even if they did, they are in space and there is no air to intake.
The gravity on the asteroid seems Earth-normal. It should be much less.
Tucker and Mayweather transport a small asteroid onto the Enterprise to harvest its resources. Seconds after it arrives, Tucker picks it up and sets it aside. If it had just been beamed aboard from space it would have been extremely cold and he would not have been able to pick it up.
When Vulcans have started flooding the room with "hexafluorine" gas the characters continue to speak normally. Hexafluoride compounds are much denser than air and cause sound waves to travel more lowly, which would make their voices sound much deeper. This would be the opposite effect of inhaling helium and then speaking.
However, whatever gas is being used, it hasn't completely replaced the air in the room before the team escapes. Moreover, the gas may not be completely a hexafluoride compound. In the short time before they escape, it hasn't completely replaced the air in their lungs and vocal tracts, so their voices wouldn't change significantly.
Reed states that T'Pol's phase pistol is set to kill but there is no way tell that from the front. The settings are at the rear.
T'Pol says that she recognizes the transponder frequency of the Vulcan ship. All transponders need to be on the same frequency otherwise they would never be heard. She might recognize the code, which would be unique.