Charge transport characteristics of short double-strand DNA including mismatches are studied within a methodology combining molecular-dynamics (MD) simulations and electronic-structure calculations based on a fragment orbital approach. Electronic parameters and transmission probabilities are computed along the MD trajectory. We find that in the course of the MD simulation the energetic position of frontier orbitals may be interchanged. As a result, the highest-occupied molecular orbital can temporarily have a large weight on the backbones as a function of time. This shows that care must be taken when projecting the electronic structure onto effective low-dimensional model Hamiltonians to calculate transport properties. Further, the transport calculations indicate a suppression of the charge migration efficiency when introducing a single GT or AC mismatch in the DNA sequence.