The thing that bothered me the most was how The Legion of Super Heroes were whining about how all of the history and culture of Earth was lost in the future. If you go back in time all the way to the beginning of Earth's cultural history and decide to sleep all the way through till you reach your own time line "Shut the F up!" There was nothing stopping them from sampling the culture and history all along the way, make recording, take books, go to a Shakespeare play or a Bon Jovi concert. They certainly don't seem to be too worried that their ship will be destroyed, archive the past to enrich the future or "Shut the F up"!
P.S. Why didn't they throw Alex in the tank, her leg would have been healed in an hour.