It is anticipated that a number of techniques to measure the top quark mass at the LHC will yield m top with uncertainties of about 0.5 − 1 percent. These uncertainties are mostly theoretical; they are usually estimated using parton shower Monte Carlo programs whose reliability at this level of precision is difficult to assess. The goal of this paper is to contrast those estimates with the results of NLO QCD computations for a few observables, often discussed in the context of high-precision top quark mass measurements at the LHC. In particular, we study the NLO QCD corrections to the invariant mass distribution of a charged lepton and a B-meson in lepton+jets channels. In the dilepton channel we investigate the invariant mass distribution of a charged lepton and a b-jet, the average energy of the two leptons and the average energy of the b-jets from top decays.