Dr. Phlox states the human and Vulcan DNA aren't compatible, then later Trip tells T'Pol that Phlox determined it was a flaw with the technique used to combine the DNA and that a human and Vulcan can have a child. They all already know this because they had a son in E² (2004).
T'Pol has short nails while holding the baby in one shot, but in the next shot a few minutes later, they have grown about an inch.
When Enterprise is traveling to the comet, the sun is to the right based on the lighting on Mars and the comet tail is pointing towards the sun on right. Comet tails always point away from sun.
When Paxton fires the beam at Earth's moon, it strikes it immediately. Even at the closest possible distance between Earth and Mars, it would take a little over 3 minutes for the beam, traveling at the speed of light, to reach the moon. The same is true for when the beam strikes the San Fransisco Bay later. (This is not a goof: a "verteron" is a particle that travels faster than light.)
When Tucker is thrown into a room by Paxton's goons, he bounces like he landed on a soft pad. When the camera tilts down as Tucker is getting up, you can clearly see the pad under him at the bottom of frame. As he moves his left leg off the pad and puts his knee on the floor, it's evident that it is several inches below the top of the pad he was just laying on.
When an engineer in engineering reports back to the bridge, an insect can be seen flying past the lamp.