The students drawings that Trip holds up look like they were made from crayons but there is no explanation how the drawings could look like a kid just drew them. In theory, they should be "printed" copies as the drawings would have been transmitted electronically from earth unless they have some type of replication technology that is not shown.
At 32 minutes one of the candles in the background goes from lit to unlit.
An ice comet with a diameter of 84 kilometers would have next to no surface gravity. There is no way Travis would have fallen down and hurt himself. There is also no way their shuttlepod would have fallen into an ice crevasse. The gravity on a comet that size would be something like 1/100th earth sea level. Even if it was a solid ball made out of the densest metal in the universe, surface gravity would still only be 0.05x that of Earth.
The characters prepare for a loud noise from the explosion on the comet, but there is no sound in space.
T'Pol says her fiance is an architect so it would be illogical for him to live in Enterprise. In 2020 people were very often working from home, so on the same principle, he could draw his designs on Enterprise then transmit (upload) them to Vulcan at the end of each Vulcan workday.
What T'Pol means is that an architect wouldn't have a role to fulfill on a starship, and hence not work and live on Enterprise. Just as in the reality of 2020, architects don't live on Navy ships, air craft carriers or submarines. Furthermore, even if an architect could most days work from home, usually the job of an architect would also entail visiting the location of each project at least once; which is unlikely to be very compatible with the mission of a starship like the Enterprise.
What T'Pol means is that an architect wouldn't have a role to fulfill on a starship, and hence not work and live on Enterprise. Just as in the reality of 2020, architects don't live on Navy ships, air craft carriers or submarines. Furthermore, even if an architect could most days work from home, usually the job of an architect would also entail visiting the location of each project at least once; which is unlikely to be very compatible with the mission of a starship like the Enterprise.
When Lt. Reed is kneeling in front of the "snowman" setting the explosive charges, there is a brief shadow across the front of the figure. But the lights are mounted on his helmet, and no part of his body is in position to cast that shadow, revealing that the real light source is behind the actor.
In the teaser, T'Pol says "We've dropped out of warp," but her lips continue to move with no further words heard.