We present state-of-the-art electronic structure calculations for the Co$_2$MnSn full-Heusler alloy. We show that in its bulk form it is a half-metallic ferromagnet with the Fermi level being located within a tiny gap of the minority-spin density of states. Moreover the alloy shows the Slater-Pauling behavior with a total spin magnetic moment in the unit cell of 5 $μ_B$. In the case of the (001) surfaces, the broken bonds at the surface form a minority band pinned exactly at the Fermi level destroying the half-metallicity. Our calculations reveal that both the interfaces with the non-magnetic metal V and the semiconductor InAs are no more half-metallic due to the different environment of the atoms of the half-metal at the interface. These interface states although localized only at the first few interface layers can become conducting when coupled to defect states and kill the spin-polarization of the current injected from the half-metal into the semiconductor or the non-magnetic metallic spacer. ; Comment: 5 pages, 4 figures Prepared for a special issue of Journal of Computational and Theoretical Nanoscience on Low-Dimensional Systems