Multi-methodological approaches combining quantum-mechanical and/or atomistic simulations with continuum methods have become increasingly important when addressing multi-scale phenomena in computational materials science. A crucial aspect when applying these strategies is to carefully check, and if possible to control, a variety of intrinsic errors and their propagation through a particular multi-methodological scheme. The first part of our paper critically reviews a few selected sources of errors frequently occurring in quantum-mechanical approaches to materials science and their multi-scale propagation when describing properties of multi-component and multi-phase polycrystalline metallic alloys. Our analysis is illustrated in particular on the determination of i) thermodynamic materials properties at finite temperatures and ii) integral elastic responses. The second part addresses methodological challenges emerging at interfaces between electronic structure and/or atomistic modeling on the one side and selected continuum methods, such as crystal elasticity and crystal plasticity finite element method (CEFEM and CPFEM), new fast Fourier transforms (FFT) approach, and phase-field modeling, on the other side.