We present an approach that combines the local-density approximation (LDA) and the dynamical mean-field theory (DMFT) in the framework of the full-potential linear augmented plane-wave method. Wannier-type functions for the correlated shell are constructed by projecting local orbitals onto a set of Bloch eigenstates located within a certain energy window. The screened Coulomb interaction and Hund.s coupling are calculated from a first-principles constrained random-phase approximation scheme. We apply this LDA+DMFT implementation, in conjunction with a continuous-time quantum Monte Carlo algorithm, to the study of electronic correlations in LaFeAsO. Our findings support the physical picture of a metal with intermediate correlations. The average value of the mass renormalization of the Fe3d bands is about 1.6, in reasonable agreement with the picture inferred from photoemission experiments. The discrepancies between different LDA+DMFT calculations (all technically correct) which have been reported in the literature are shown to have two causes: (i) the specific value of the interaction parameters used in these calculations and (ii) the degree of localization of the Wannier orbitals chosen to represent the Fe3d states, to which many-body terms are applied. The latter is a fundamental issue in the application of many-body calculations, such as DMFT, in a realistic setting. We provide strong evidence that the DMFT approximation is more accurate and more straightforward to implement when well-localized orbitals are constructed from a large energy window encompassing Fe-3d, As-4p, and O-2p and point out several difficulties associated with the use of extended Wannier functions associated with the low-energy iron bands. Some of these issues have important physical consequences regarding, in particular, the sensitivity to the Hund.s coupling.