Plot hole: Clint Eastwood's whole investigation/solution is based on him suspecting that the victims had a common tie, rather than being random. The problem is there is no reason for him to think this - there is no reason given for them to not be considered random victims. For him to think otherwise was a bit far fetched. In the book, however, they were all on the organ donor list, which led him to the fact they all had the same rare blood type and so on.
Suggested correction: Not really farfetched. It's a common plot device for a cop to look for a link. When he finds out Gloria gave blood, he remembered the sticker in the other victim's car.
Plot hole: When Austin and his father Nigel disagree as to how to proceed after Goldmember gets away, they part ways. So why does Austin take his father's car? (01:06:25)
Plot hole: When Alexander is traveling into the future and goes through the ice age he is visibly affected by the extreme cold temperature outside the time bubble. However when he stops in the future when the moon had been destroyed then continues he is not affected by the explosions and extreme heat around him. Based on the effect the extreme cold had on him (frost on his face and hair) he should have been roasted alive.
Plot hole: Throughout the movie, the flies are vulnerable to light (direct sunlight and even lightbulbs) to the point of incinerating in a split second. Except... they are not; in several sequences they fly to and from bodies and without even taking a direct path (look at all the action happening in front of the house, by the cars, in broad daylight).