Two things right away (I am sure I could find more if I try):
1. Closed cycle life-support system aboard each ship. Maintaining a closed biosphere is a HARD problem -- and one usually glossed over by space cadets. We are no closer to it than to AI. Actually, that is discussed at length in Stross' page.
2. When 10 people get to Alpha Centauri, what do you expect them to do there? To maintain a viable population you need thousands, to maintain a self-sustaining indistrial civilization, millions. First problem can be solved with genetic engineering, and second with strong AI and self-reproducing technology, but that puts you well outside "almost current" technology.