As-grown crystals of Fe(Te,Se) do not show bulk superconductivity due to the presence of excess irons. Annealing in an appropriate atmosphere can remove harmful excess irons and make them bulk superconductors. We report the effects of annealing on Fe1+y(Te0.6Se0.4) crystal in chalcogen (O2, S, Se, Te) and pnictogen (P, As, Sb) atmospheres. It is found that the optimal molar ratios of agents to the total irons are different for different agents, indicating that different mechanisms for the removal of excess irons are operative. The normal state and superconducting properties of optimally annealed crystal are carefully investigated. Critical current density and its relaxation measurements clarified that the vortex dynamics in Fe1+y(Te0.6Se0.4) is described by collective creep theory. Detailed analyses of the temporal evolution of the critical current at various temperatures clarified that the pinning of vortices in Fe1+y(Te0.6Se0.4) is a combination of $\Delta T_{\mathrm{c}}$ and $\Delta l$ pinnings.