We have observed the planetary nebula NGC 2440 in the transitions [O II] λ3727, He II λ4686, [O III] λλ(4363+5007), H I λλ(4861+6563), He I λ5876, [N II] λ6584, [S II] λλ(6717+6731), and [S III] λ9061, as well as in various continuum filters. As a result, we are able to evaluate the excitation structure of the source and determine the projected variations in density, extinction, and temperature. Density is found to have a bilobal structure at the nucleus, where peak values approach 2×103 cm-3, and thereafter decline to ~500 cm-3 for distances ~+/-12" from the central star. Densities for larger spatial offsets appear more uniform, although the maps reveal evidence for appreciable small-scale clumping. Electron temperatures appear to vary by no more than ΔTe/Te~0.035 throughout much of the shell, although here again Te rises by ~14% a little to the southeast of the nucleus, an enhancement which may also extend northwest and southeast along P.A.=135deg. Finally, it is noted that, as in the case of extinction and density, the extinction is prone to small but quite rapid variations over the projected surface of the source by of order ΔAv~+/-0.1 mag. There appears to be evidence for a band of extinction with amplitude ΔAv~0.2 mag along the minor axis of the exterior bilobal flow and for a possible extinction deficit associated with the interior bilobal flow. We discuss possible scenarios for the formation of this multipolar nebula in the context of the present results.