Well it doesn't state specificaly in the DMG, do the slippers of spiderclimbing enable movement through web (natural or magical)? Also, does anyone besides me think that casting while entangled in webs (natural or magical) should require a concentration check?
As to the slippers, I don't see why they would. The spider climb spell doesn't give you such freedom, and unless the slippers specifically give you that power, you shouldn't get it.
As for the entanglement, in magical webs, you do have to make a Concentration check to cast spells(DC 15+spell level.) It may not be spelled out in the Web spell, but Web makes you entangled, an affect which is spelled out in the glossary of the PH. As far as natural webs, it is, as always, up to the DM whether this would classify as being entangled, and hence requiring a Concentration check.