The tables in the mess area of the Horizon are identical to those seen in the mess of Star Trek Voyager.
T'Pol is being polite, accepting and eating the popcorn that Archer offers her at the movie night. As has been previously explained in the season one episode "Shadows of P'Jem", Vulcans don't eat with their hands.
Mission Date: January 10, 2153
Nitpick: Travis tells his brother that he'll ask Malcolm to help remove the homing beacon from the Horizon's hull. However, upon coming back aboard Enterprise, Travis makes no such request, and even hides from Archer that they had trouble with any hostile aliens.
Nitpick: Archer tells Mayweather that his father had recommended him for the position, and both act as if this is the first time he has shared this information. However, Archer had previously revealed this in the first season.
Trip: We're going to be showing three of the greatest horror movies ever made - Frankenstein, Bride of Frankenstein, and Son of Frankenstein. We might even throw in Abbott and Costello Meets Frankenstein.
T'Pol: Captain, I'm reading biosigns on the planet. To quote Dr. Frankenstein, "It's alive."
Paul: Maybe you can stop by engineering... build us a warp 5 engine.
Mayweather: Starfleet really oughta think about putting families on starships.
Reed: You must be joking.
Mayweather: No one would ever get homesick.
Reed: Yes? Well they'd better post a psychologist on board because I'd need one if my parents were roaming the corridors.