Molecular dynamics simulation is performed for the liquid metal potassium. Using the set of liquid-glass structure factors obtained from the simulation, we study the glass transition temperature by (a) dynamically solving the non-linear integral equation for the density-density correlation function in the context of the mode-coupling theory. (U. Bengtzelius, W. Götze and A. Sjölander, J. Phys. C, 17 (1984) 5915) and (b) structurally calculating the Wendt-Abraham parameter (H.R. Wendt and F.F. Abraham, Phys. Rev. Lett., 41 (1978) 1244). It is found that the glass transition temperature obtained from the former is distinctly higher than that from the latter. In an attempt to explain this difference in glass transition temperature, we draw attention to some recent works on shear viscosity coefficient measurement and discuss the latter results in the light of the basic hypothesis of the mode-coupling theory. It appears that the glass transition point obtained in the context of the mode-coupling theory for metallic potassium is predicted reasonably and that the glass transition point determined directly from the Wendt-Abraham structural data seems numerically closer to the calorimetric glass transition temperature. Also, we compare the metallic Debye-Waller factor obtained from the present molecular dynamics simulation with the corresponding asymptotic formula proposed in the mode-coupling theory (W. Götze and L. Sjögren, Rep. Prog. Phys., 55 (1992) 241); they are found to agree reasonably well with each other. The role of the pair potential in the non-ergodicity form factor is also discussed briefly both for a hard sphere fluid and for the metallic potassium system.