[en] We study the effect of disorder, including swap and antisite, on the electronic and magnetic properties of heterostructures by using extensive first-principles calculations within density functional theory. Thirteen kinds of swap disorders and sixteen kinds of antisite disorders are proposed and studied comprehensively. Our calculation reveals that disorders at the interface have low formation energies, indicating that disorders are most likely to appear at the interface instead of the deep layer. Among all kinds of disorders, Mn"1(Al) (where the interface Mn is occupied by an Al atom) and Mn"1(As) (where the interface Mn is occupied by an As atom from a GaAs slab) antisite disorders possess the lowest formation energies. This shows that the interface Mn has a higher probability of being replaced by an Al atom, and that an As atom from a GaAs slab easily diffuses into a Mn_2CoAl slab and occupies the position of the interface Mn. Moreover, further study on the interface electronic structure reveals that interface spin polarization suffers dramatic reduction due to Mn"1(Al) and Mn"1(As) antisite disorders. It can be deduced that the interface state, together with Mn"1(Al) and Mn"1(As) antisite disorders, may be the main causes of the low TMR ratio of Mn_2CoAl/GaAs heterostructures. (paper)