Deliberate mistake: After Doug finds where Minuti was killed and set on fire, he walks over to a dock where he sees Minuti's arm being eaten by alligators. Minuti had been dumped in the water 4 days prior, yet his hand is perfectly intact with no signs of burning, bite marks or weather/water damage of any kind.
Deliberate mistake: When Doug is in the Hummer chasing the terrorist, you are given a first person perspective of Doug wearing the goggle rig. A split screen shows one view (his right eye) of present day, and the other, 4 days in the past (his left eye). If you look closely, the present day shot will pan right and the other shot will pan left, yet they should be looking in the same direction at all times.
Answer: The second part of your question: the bad guy needed a truck. He called Claire but they can't deal. SO he bought another truck. That truck shot by the policeman. Because he don't have enough time he must call Claire again to buy her truck.