(1)∵集合U={0,1,2,3},A={x∈U|x2+mx=0},?UA={1,2},∴A={0,3},由A中方程变形得:x(x+m)=0,解得:x=0或x=-m,可得-m=3,解得:m=-3;(2)∵A是单元素集,∴A中方程△=0,即m2=0,解得:m=0.