Dear foxdog175, you are absolutely right: you do have semitransparent pixels in your layers after resize. It's an inherent effect of resize. Photoshop shows selection border (so called "marching ants") at 50% level of transparency of the current selection. And after resize it is not actually the same as before resize. It's blurred. Enter the Quick Mask mode and you'll see it yourself.
In your case I don't think there is an ultimate solution. You could try something, though. Don't bother with clone tool. You could try and boost the transparency of border pixels in your layers up to 100%. Unfortunately, Photoshop does not let do it easily(this feature has been in need for SO long, all to nothing). But you could use some filters. For example, the Synthetic->Filter Factory. Enter (a>0)? 256: 0 in the alpha channel field of the filter dialog and all semitransparent pixels would become absolutely opaque.
Of course, there still could appear overlap between your layers(they can be fixed). And there still could appear missing pixels, if you're really out of luck, that is(they can be fixed too).
But this is at least something you can try...
Or just merge your layers to a separate layer before resize and make them all over again after resize, using their transparencies.
Or use some non-interpolation method, like Nearest neighbor for your layers.



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(they can be fixed too). 



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