Flaw in the science

I think they actually got the science backwards with regards to the gravity gun. If Lex was experiencing a strong gravitational field (created by the gravity gun), then his clock would slow down, not speed up. The "deeper" you are in a gravitational field, the slower your clock is in comparison to people that aren't as deep in the gravitational field. This fact is important for GPS satellites (being so high above Earth, gravity is a bit weaker there than it is for the people standing on Earth's surface, and this difference in gravitational strength causes a difference in time-keeping which must be properly accounted for in order for GPS devices to accurately determine distances and triangulate locations). So Lex's super powers would've lasted more time (from the point of view of everyone else), not less time as portrayed in the movie.

For more details, check out: http://en.wikipedia.org/wiki/Gravitational_time_dilation

It's true that Superman would've needed to travel faster than light to get to a nearby star and back in anything under ~8 years. If he travels faster than light, some really weird stuff could happen, like arriving at a point in the past before the time he left. See for example: http://en.wikipedia.org/wiki/Tachyonic_antitelephone

You got it backwards. When a person travels near light speed, time slows down for him, not the rest of us. So Superman may have only aged a day or two while months passed on Earth.

It's a story about a dude from another planet who flies around in a leotard and red boots. Don't worry too much about the science.