The satellite dishes on the communications building are pointed slightly up. Satellites orbit near the equator, so satellite dishes in Alaska point horizontally, or slightly down. For that reason, it's not likely that the characters would have satellite phones.
Everyone is eager to get the "last flight out" before the airport closes down for 30 days. The airport may close for occasional storms, but it never shuts down for 30 days. Alaska Airlines flies to Barrow at least once a day all year.
In the film, Barrow is bright and sunny one day, then completely dark for the next 67 days. In reality, the days get shorter and shorter until the sun no longer appears over the horizon. Twilight appears every day, between noon and 4:00 pm, until the sun once again peeks over the horizon.
UV rays are harmful to plants, so grow lamps don't emit any more UV light than regular fluorescent lights. Either the light should've killed the plants, or the vampires should've suffered burns from normal lighting.
Most indoor and street scenes are well-lit, despite having no sunlight or electricity. Even if the buildings had their own generators, which doesn't explain the streets, the characters were trying to avoid detection that lights would certainly bring.
During the blizzard, when the group is moving from the attic to the general store, the wind is raging, yet the power lines are not moving. No ice has accumulated on the lines, so they aren't frozen solid.
The goof items below may give away important plot points.
When Eben is about to inject himself with Billy's blood, he says that Riis and Carter were bitten, but they were actually scratched. Riis was scratched during his struggle with the vampires; the mark on Carter's face is clearly a scratch rather than a bite. Also, Billy was changing right after being bitten by Arvin, which implies Eben was wrong about the bitten being able to retain their humanity for a while longer.