In the first scene, where the man and woman are being chased through a tunnel, the man wears a thick down jacket in the first shot. In the second shot he just wears a sweater. In the third shot he wears his jacket again. When they finally reach the door, he is just wearing his sweater again.
At the end when leaving the colony there are clearly 4 people then instantly 5. After a quick scene in a new location there are 5 shown then instantly 11.
In the beginning of the movie a wind turbine is seen with wings having their trailing edge into the wind instead of its leading edge. The wings are either constructed for counter-clockwise rotation (in the movie the turbine rotates clockwise) or are pitched around 180 degrees. Either way, the turning of the turbine is impossible with this blade configuration.
When they exit colony five, Laurence Fishburne's character explodes the chimney from which they climbed out by throwing a pack of dynamite inside of it. In the next cut we see the chimney going off, but it explodes at ground level, making it collapse, not underground, where the dynamite should have fallen by that time.
The bridge is shown over a crevasse with a glacier flowing through, around the bridge supports. A glacier would have destroyed the supports.
At the beginning when the group of three cross the bridge, they cross it on the "street level" where the cars used to pass. But in the next angle, when we see that side of the bridge where they were heading from above, we can see the tops of street lights poking out from the snow in the same level.
Crazed cannibals or not, the people in the remote site were still human beings with human weaknesses. Being shot in the torso with a .30 rifle round would seriously injure or kill them, regardless of how "psyched up" that they were.
If it were indeed cold enough to maintain almost constant snow, ice and cold as well as glaciers, then it would be too cold for the cannibals to travel far in without proper winter gear or head coverings. Hypothermia can set in within 30 minutes and the distance back to The Colony seems to be measured in dozens of miles.
Towards the beginning when they cross the bridge there is almost no snow on the bridge. The bridge should be completely frozen and covered in snow, not the clearest and least frozen place they hike through.
When Briggs removes the handgun from the hand of a frozen body, its arm moves when it should actually be frozen stiff.
During both trips across the bridge, the characters jump over chasms in the roadway where the surface had broken away. They could just as easily have walked on the supporting beams at the edges of the roadway.
When Briggs and Sam are crossing the bridge Briggs sets explosives to destroy a section of the bridge to stop the advance of the cannibals chasing them. They run a few yards and then shield themselves from the explosion behind debris, but they could have - and should have - kept running.
The bridge, as others have pointed out, either would not be there given the glacier flow or would be encased in ice and snow. But assuming it as seen and given how long they have been living in the environment, the travellers would walk along the outside steel structure rather than risking the obviously fragile roadway and in any case would be carrying ropes and using team roping to secure against individual slips & falls when crossing such an obstacle.