Mass loading of reflective foils
Albedo or reflectivity of thin foils
Deployment of thin films
Extra mass of booms, deployers, etc
Survival of thin films in hostile environment of UV, flares, particle radiation, charging "packageability, areal density, structural stability, deployability, controllability, and scalability...strength, modulus, areal density, reflectivity, emissivity, electrical conductivity, thermal tolerance, toughness, and radiation sensitivity."
Unfortunately, light weight sails must also be very thin. And that leads to a host of other problems. The deployment of ultrathin foils without tearing or crumpling is a major issue. Then there are the environmental problems of UV and particle radiation in space that are known to convert plastic into so much brittle parchment, much like the rear window of convertibles.
Solar sails may one day be a viable means of interstellar travel, but not right now, as the problems with solar sails are immense.
All that is necessary is that we build a ship big enough for people to breed aboard, say, inside an astroid with a wide eliptical orbit, and kick it out of orbit and on it's merry way with some kind of currently available thrust. If you have all the time in the world, you don't need very advanced technology. If you want to get to Beta Centauri by tomorrow noon on a regularly scheduled intersteller cruiser, that might not be in the cards. But, that wasn't the question asked.