Is it possible to put SMT components on both sides of the board with the pads touching? I don't want the pads to be electrically connected, but my PCB program (gEDA PCB) warns that they are shorted. Is there any way to avoid this?
It's done all the time, the software I use doesn't give a warning. Contact the support people for your PCB software, they should tell you how to avoid the problem. Or, just ignore the warnings, the boards should come out OK. You could check the Gerbers with a program like GC-Prevue to make sure.
Are you sure the pad definitions are OK, and the parts are actually placed on different sides? - it shouldn't give a warning about pads on different layers touching.
Make sure the pads don't have any vias in them. I have seen some component footprints that have vias on their pads and I don't realize it until it comes to fab.
I have also seen footprints in our corporate database that have been made with keep out markers that go to all layers causing DRC errors when I put components top to bottom.
Probably unlikely any of these are your issue, but at least something to check.