Hmmm… I don’t see much solution besides adding some loop cuts and using “Remove Doubles”.
However, you can make things easier for you. Your mesh is symmetrical on the 3 axes (if you ignore the fact that the lower panes are taller). My first step would be to add some loops cuts and to delete vertices to be able to use a Mirror modifier. That will divide your workload by 8.
Next step is to resize your boxes so that they overlap only on edges, i.e. so that no vertex is a middle of a face of another box. Then you create enough loop cuts to have vertices at every corner of the overlapping parts. After all this, you can to use “Remove Doubles”.
But your work isn’t over yet. You must then disable the Mirror modifier (and hide the glass) to delete all the useless faces inside your mesh.
The next step is to merge the useless vertices in the corners. Then you apply the mirror modifier and delete the loop cuts on the 3 axes. And finally, you can pull all the bottom vertices in one move to resize the bottom panes.
I’m a little worried tho when I see your grid floor in the background and the directions pointed by the arrows of the 3D manipulator. Did you work in local coordinates at a random angle? In that case, there is only one magic formula: Head, wall, bang!.. Restart.
One final word: Inflatable. If your mesh doesn’t look like an inflatable… structure (No, no, I won’t say inflatable doll!) then it’s wrong. Loops cuts, insets and extrusions! That’s the way of the mesh, Little Grasshopper.