My short-term worry about basic income is that it'll end up bidding up the prices for goods that poor people buy, especially the rent. I won't be surprised if most of the basic income eventually goes to the landlords. IMO the right solution is to get the government involved in distributing certain goods, not just handing out money to buy them. The state could guarantee free housing, food, healthcare, education and pensions for everyone, on top of basic income for spending money. The USSR managed that with a fraction of the resources.
My long-term worry about basic income is that people have a need to be needed by society and it won't go away easily. I don't know a good way to solve that completely, short of reengineering humanity. In the short term we could get away with making the government pay companies for employing people (the payment should be lower than the salary, but maybe not by much). That could be a nice supplement to basic income.